# Area as an Anti-Derivative: Derivation of the FTC
# Yasskin & Meade for WebALT 2006

# ##################################
# # Header For All Maplets
restart:
with(Maplets[Elements]):with(Maplets[Tools]):
StartEngine();
randomize():

lightorange:="#FFB300":
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lightblue:="#CFCFFF":
lightgreen:="#CCFFCC":
darkgreen:="#00C000":
ColorBkgd:=wheat:
ColorDefaultMenu:=lightcyan:
ColorHelpMenu:=lightorange:
ColorFileMenu:=pink:
ColorFooter:=lightcyan:
ColorNewButton:=magenta: # or Make, Save, Enter Problem
ColorReturnButton:=magenta:
ColorCloseButton:=pink: # or Quit, Clear, Reset, Cancel
ColorHintButton:=lightorange: # or Syntax
ColorPrevButton:=turquoise: # or Update
ColorEnterButton:=turquoise:
ColorSimplifyButton:=lightorange:
ColorCheckButton:=green:
ColorShowButton:=lightorange:
ColorPlotButton:=gold: ColorPlotButtonFrgd:=black:
ColorPlotFrame:=gold:
ColorTableBkgd:=lightgreen:
ColorCalculatorBkgd:=gold:
ColorBlackBox:=black: ColorBlackBoxFrgd:=yellow:
ColorMessage:=white: ColorMessageFrgd:=black:
ColorInput:=turquoise: ColorInputFrgd:=black:
ColorCorrect:=green: ColorCorrectFrgd:=black:
ColorIncorrect:=red: ColorIncorrectFrgd:=white:
ColorWarning:=yellow: ColorWarningFrgd:=black:
ColorShow:=lightorange: ColorShowFrgd:=black:
ColorHint:=lightorange: ColorHintFrgd:=black: # or Info, Syntax
ColorDisable:=wheat: ColorDisableFrgd:=black:
FontFooter:=Font("helvetica",10):
FontSymbol:=Font("symbol",12):
FontBig:=Font("times",20):
#LIBLogo:=cat(libname,"/M4C/M4C.png"):
#Logo:="M4C.png":
LIBLogo:=cat(libname,"/M4C/WebALT_logo.png"):
Logo:="WebALT_logo.png":

# ##################################
# # Template Translation Table For All Maplets
TEXTLprogrammers:=
"Programmers: D.B. Meade & P.B. Yasskin":
TEXTLcopyright:=
#"© Copyright: Maplets for Calculus 2006-10":
"© Copyright: WebALT 2006-07":
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"M4C v1.3 July 2010":
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"diverges   ":
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"Divergent":
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"Modify or Make Your Own Problem":
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"ymax =":
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" Please be patient while the plot is generated.":
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" You must enter an expression to be expanded.":
TEXTreplyNoNormalize:=
" You must enter an expression to be normalized.":
TEXTreplyNoModify:=
" You must enter an expression to be modified.":
TEXTreplyNoPlot:=
" Please select a plot.":
TEXTreplyNoSelection:=
" Please select an answer.":
TEXTreplyNoSaveProblem:=
" You must fill in all the boxes before saving the problem.":
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" Both sides of your inequality are wrong.":
TEXTreplyNoConst:=
" You forgot to add a constant of integration.":
TEXTreplyManyConst:=
" Your answer should have only one constant of integration.":
TEXTreplyMinusErr:=
" You have a minus sign error.":
DNEset:=
{"", undefined, Undefined, UNDEFINED, divergent,  Divergent,  DIVERGENT, diverges, Diverges, DIVERGES, dne, DNE, doesnotexist, DoesNotExist}:

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great:=[
" Bullseye.",
" Right on the mark.",
" Great.",
" That's absolutely right.",
" Awesome. You're unstoppable.",
" Correct.",
" WOW, nailed that one.",
" You got it!",
" YES! Right on.",
" Way to go.",
" Don't stop now.",
" I knew you could do it!",
" Perfect. You're unstoppable.",
" Radical Dude.",
" Power house.",
" Sweet! Keep on Rockin'.",
" You rock!",
" You got those mad skills.",
" Awesome!",
" Wowzers! That was great!",
" Awesome man!",
" Good job! You really know what you are doing.",
" You're awesome kid.",
" Tearing it up.",
" Right on the money.",
" High Five!!!!!",
" Cool Beans.",
" What a nerd!",
" You're so money.",
" You're a genius.",
" You hit the nail on the head.",
" Excellent!",
" If I had a cookie, I'd give it to you.",
" You're a winner.",
" That's a winner.",
" Whoop! Way to go.",
" That's the way, ah ha ah ha, I like it.",
" Oh yeah!",
" You're the bomb!",
" That was fantastic!",
" Oh Snap!",
NULL
]:
nextgeneric:=[
" Keep it up.",
" Keep going.",
NULL
]:
nextprob:=[
" On to the next problem.",
" Try another problem.",
" You're ready for another problem.",
NULL
]:
nextquest:=[
" On to the next question.",
" Try another question.",
" You're ready for another question.",
NULL
]:
nextpart:=[
" On to the next part.",
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" You're ready for another part.",
NULL
]:
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" On to the next step.",
" Try another step.",
" You're ready for another step.",
NULL
]:
nexteq:=[
" On to the next equation.",
" Try another equation.",
" Solve another equation.",
" You're ready for another equation.",
NULL
]:
nextfn:=[
" On to the next function.",
" Try another function.",
" You're ready for another function.",
NULL
]:
nextlim:=[
" On to the next limit.",
" Try another limit.",
" Compute another limit.",
" You're ready for another limit.",
" Find another limit.",
NULL
]:
nextderiv:=[
" On to the next derivative.",
" Try another derivative.",
" Compute another derivative.",
" You're ready for another derivative.",
" Differentiate another function.",
NULL
]:
nextinteg:=[
" On to the next integral.",
" Try another integral.",
" Compute another integral.",
" You're ready for another integral.",
" Integrate another function.",
NULL
]:
nextdiffeq:=[
" On to the next differential equation.",
" Try another differential equation.",
" You're ready for another differential equation.",
" Analyze another differential equation.",
NULL
]:
nextseq:=[
" On to the next sequence.",
" Try another sequence.",
" Find the limit of another sequence.",
" You're ready for another sequence.",
NULL
]:
nextser:=[
" On to the next series.",
" Try another series.",
" Sum another series.",
" You're ready for another series.",
NULL
]:
almost:=[
" Close.",
" Oh so close.",
" Close call. ",
" Near miss.",
" Not quite good enough for government work.",
" Ooooh...close.",
" Yikes! Really close. You'll get it next time.",
" Close, but no cigar.",
" Slightly off.",
" Off by a hair.",
" Almost there.",
" Almost got it.",
NULL
]:
sorry:=[
" Sorry, that's not right.",
" Nope, but don't give up.",
" Not quite, it's a little off.",
" Bummer, thought you would get it this time.",
" If you need help, please ask a human.",
" I don't know where you went wrong.",
" Sorry, killer problem.",
" No, but don't blow it off.",
" D'oh!",
" That's whack.",
" Thought you would get it this time.",
" Nice try, but your answer is wrong.",
" Ask your neighbor for help.",
" Brutal kid.",
" That won't fly.",
" So close and yet so far.",
" So, that was just practice.",
" A swing and a miss.",
" Better luck next time.",
" Oops.",
" Tilt. Play again.",
" I know you can do better.",
" Sorry Charlie.",
" Tisk, tisk. It's a tough one.",
" It takes a lot of wrongs to make a right.",
" Even Einstein didn't get everything right.",
" Today's not your lucky day.",
" Don't quit your day job.",
" You're colder than a polar bear's toenail.",
op(almost),
NULL
]:
trygeneric:=[
" Fix your answer and check it again.",
" Give it another try.",
" Try again.",
" Please try again.",
NULL
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" Try the hints and answer again.",
" Read the hints and try again.",
" Study the hints and answer again.",
NULL
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" Look at the Help menu and try again.",
NULL
]:
showgeneric:=[
" OK That's just practice. But try doing it yourself.",
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NULL
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NULL
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showhelp:=[
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NULL
]:

# ##################################
# Procs for all maplets.
GetVersion:=proc()
local S, S1, S3, S4;
options `Copyright 2009-10, Philip B. Yasskin and Douglas B. Meade, Maplets for Calculus`;

uses StringTools;
S:=interface(version);
S:=map( Trim, Split( S, "," ) );
S1:=Split(S[1], " " );
S3:=Split(S[3], " " );
S4:=Split(S[-1], " " );
sprintf("%s (%s)", S[2],S3[-1]);
end proc:

# ##################################
# # Customize For Each Maplets
with(plots):with(plottools):
#with(RandomTools):
#alias(e=exp(1)):
nextlocal:=[
NULL
]:
trylocal:=[
NULL
]:
showlocal:=[
NULL
]:
nexts1:=[ #Keep what is appropriate. This is for all but the last check.
op(nextgeneric),
op(nextprob),
op(nextquest),
op(nextpart),
op(nextstep),
op(nextlocal),
NULL
]:
#nexts2:=[ #Keep what is appropriate. This is for the #last check.
#op(nextgeneric),
#op(nextprob),
#op(nexteq),
#op(nextfn),
#op(nextlim),
#op(nextderiv),
#op(nextinteg),
#op(nextdiffeq),
#op(nextseq),
#op(nextser),
#op(nextlocal),
#NULL
#]:
trys:=[ #Keep what is appropriate.
op(trygeneric),
op(tryhint),
#op(tryhelp),
op(trylocal),
NULL
]:
shows:=[ #Keep what is appropriate.
op(showgeneric),
op(showhint),
#op(showhelp),
op(showlocal),
NULL
]:
randgreat:=rand(1..nops(great)):
randnext1:=rand(1..nops(nexts1)):
randnext2:=rand(1..nops(nexts2)):
randalmost:=rand(1..nops(almost)):
randsorry:=rand(1..nops(sorry)):
randtry:=rand(1..nops(trys)):
randshow:=rand(1..nops(shows)):

# ##################################
# # Translation Table For AreaDerivFTC
TEXTLasstprogrammer:=
"Assistant Programmer: Matthew Barry":
TEXTtitleMAIN:=
"Area as an Antiderivative: Derivation of the Fundamental Theorem of Calculus":
TEXTDiffHint:=
" A(x+h)-A(x)  is the area under the curve. It is approximated by the area of the rectangle.\n So enter the area of the rectangle.":
TEXTSlopeHint:=
" Divide the previous approximation by h.":
TEXTDerivHint:=
" Notice that the previous approximation is independent of h.":
TEXTreply1a:=
" You gave the height of the rectangle. You need the area. ":
TEXTreply1b:=
" You gave the width of the rectangle. You need the area. ":
TEXTreply2a:=
"That's the numerator. Don't forget to divide by h. ":
TEXT0a:=
" Let  A(x)  be the area below  y = f(x),  above the  x-axis,  between  a and x.\n It is shown in magenta.":
TEXT1cap:=
"Goal:  To compute the derivative of the Area function,  A'(x).":
TEXT1a:=
"\n Its definition is:":
TEXT1b:=
" The quantity  A(x+h)  is the area of the region\n below  y = f(x), above the  x-axis, between  a and x+h,\n It is shown in magenta and green. Click on Play.":
TEXT1c:=
" The quantity  A(x+h) - A(x)  is the area of the region below  y = f(x),\n above the  x-axis,  between  x and x+h.  It is shown in green.":
TEXT1d:=
" The quantity  A(x+h) - A(x)  may be approximated by the\n area of the rectangle with height f(x)  and  width h.\n It is shown in blue. Click on Play.":
TEXT1e:=
" Notice the approximation gets better as h gets smaller.":
TEXTCBPlotArea:=
"Plot A(x+h)":
TEXTCBPlotRect:=
"Plot Rectangle":
TEXT3cap:=
"Derivation:":
TEXTtitleFTC:=
"The Fundamental Theorem of Calculus":
TEXT4a:=
"You have just justified one version of the Fundamental Theorem of Calculus which states:":
TEXT4b:=
"    The Fundamental Theorem of Calculus    ":
TEXT4c:=
" If  f(x)  is a positive function and  A(x)  is the area under the graph of  y=f(x),  above the x-axis,  between  a and x,  then  A(x)  is an antiderivative of  f(x),  that is,  A'(x) = f(x).":

# NULL;

fx:=sin(2*Pi/10*(x-1))+3-x/10:
p0:=plot(fx, x=-1..10, color=black):
t0:=textplot([9,4,"y = f(x)"]):
plotseq:=NULL:
for theta from 0 by 1/12 to 23/12 do
  p1:=plot(fx, x=1..5+3*sin(theta*Pi), color=magenta, filled=true):
  t1:=textplot([[1,0,"a"],[5+3*sin(theta*Pi),0,"x"]], align=BELOW):
  t2:=textplot([3+3/2*sin(theta*Pi),1.5,"A(x)"]):
  plotseq:=plotseq, display([p1,p0,t2,t1,t0],
    view=[-1..10,-1..4.5],
    tickmarks=[0,0], labels=["",""]):
end do:
d00:=display([plotseq], insequence=true):
p1:=plot(fx, x=1..5, color=magenta, filled=true):
pfx:=plot(subs(x=5,fx), x=0..5, linestyle=DOT, color=black):
t2:=textplot([3,-.4,"A(x)"], align={BELOW}, color=magenta):
t3:=textplot([5,1.5,"A(x+h)"]):
t4:=textplot([5,-.4," A(x+h) - A(x)"], align={BELOW,RIGHT}, color=green):
tfx:=textplot([0,subs(x=5,fx),"f(x) "], align=LEFT):
plotseq:=NULL:
for H from 3.1 by -.2 to 0.1 do
  t1:=textplot([[1,0,"a"],[5,0,"x"],[5+H,0,"x+h"]], align=BELOW):
  p2:=plot(fx, x=5..5+H, color=green, filled=true):
  plotseq:=plotseq,display([pfx,p2,p1,p0,tfx,t4,t3,t2,t1,t0],
    view=[-1..10,-1..4.5],
    tickmarks=[0,0], labels=["",""]):
end do:
d10:=display([plotseq], insequence=true):
t5:=textplot([5,subs(x=5,fx)," h * f(x)"], align={ABOVE,RIGHT}, color=blue):
plotseq:=NULL:
for H from 3.1 by -.2 to 0.1 do
  t1:=textplot([[1,0,"a"],[5,0,"x"],[5+H,0,"x+h"]], align=BELOW):
  p3:=plot(subs(x=5,fx), x=5..5+H, color=blue, filled=true):
  plotseq:=plotseq,display([pfx,p3,p1,p0,tfx,t5,t2,t1,t0],
    view=[-1..10,-1..4.5],
    tickmarks=[0,0], labels=["",""]):
end do:
d01:=display([plotseq], insequence=true):
plotseq:=NULL:
for H from 3.1 by -.2 to 0.1 do
  t1:=textplot([[1,0,"a"],[5,0,"x"],[5+H,0,"x+h"]], align=BELOW):
  p2:=plot(fx, x=5..5+H, color=green, filled=true):
  p3:=plot(subs(x=5,fx), x=5..5+H, color=blue, filled=true):
  plotseq:=plotseq,display([pfx,p2,p3,p1,p0,tfx,t5,t4,t3,t2,t1,t0],
    view=[-1..10,-1..4.5],
    tickmarks=[0,0], labels=["",""]):
end do:
d11:=display([plotseq], insequence=true):
plotseq:=NULL:

PlotIt:=proc()
local PlotArea, PlotRect;
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

PlotArea:=Get(CBPlotArea::truefalse);
PlotRect:=Get(CBPlotRect::truefalse);
if PlotArea and PlotRect then
Set(PFTC=d11);
elif PlotArea then
Set(PFTC=d10);
elif PlotRect then
Set(PFTC=d01);
else
Set(PFTC=d00);
end if;
end proc:
SetSpeed:=proc()
local speed;
options `Copyright 2004-10, Philip B. Yasskin and Douglas B. Meade, Maplets for Calculus`;

speed:=600 - Get(SlSpeed);
Set(PFTC(delay)=speed);
end proc:

DiffHint:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(reply=TEXTDiffHint, reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:
DiffCheck:=proc()
local userDiff;
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

userDiff:=Get(TFDiff::anything, corrections, update);
if userDiff=f(x)*h then
  Set(TFDiffMsg=TEXTCorrect,
    TFDiffMsg(background)=ColorCorrect, TFDiffMsg(foreground)=ColorCorrectFrgd):
  Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
    reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd):
  Set(BSlopeCheck(enabled)=true, BSlopeCheck(background)=ColorCheckButton);
  Set(BSlopeShow(enabled)=true, BSlopeShow(background)=ColorShowButton);
elif userDiff=f(x) then
  Set(TFDiffMsg=TEXTIncorrect,
    TFDiffMsg(background)=ColorIncorrect, TFDiffMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(TEXTreply1a, trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
elif userDiff=h then
  Set(TFDiffMsg=TEXTIncorrect,
    TFDiffMsg(background)=ColorIncorrect, TFDiffMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(TEXTreply1b, trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
else
  Set(TFDiffMsg=TEXTIncorrect,
    TFDiffMsg(background)=ColorIncorrect, TFDiffMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(sorry[randsorry()], trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if;
end proc:
DiffShow:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(TFDiff="f(x) * h"):
Set(TFDiffMsg=TEXTShown,
  TFDiffMsg(background)=ColorShow, TFDiffMsg(foreground)=ColorShowFrgd):
Set(reply=shows[randshow()],
  reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
Set(BSlopeCheck(enabled)=true, BSlopeCheck(background)=ColorCheckButton);
Set(BSlopeShow(enabled)=true, BSlopeShow(background)=ColorShowButton);
end proc:

SlopeHint:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(reply=TEXTSlopeHint, reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:
SlopeCheck:=proc()
local userSlope;
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

userSlope:=Get(TFSlope::anything, corrections, update);

if userSlope=f(x) then
  Set(TFSlopeMsg=TEXTCorrect,
    TFSlopeMsg(background)=ColorCorrect, TFSlopeMsg(foreground)=ColorCorrectFrgd):
  Set(reply=cat(great[randgreat()],nexts1[randnext1()]),
    reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd):
  Set(BDerivCheck(enabled)=true, BDerivCheck(background)=ColorCheckButton);
  Set(BDerivShow(enabled)=true, BDerivShow(background)=ColorShowButton);
elif userSlope=f(x)*h then
  Set(TFSlopeMsg=TEXTIncorrect,
    TFSlopeMsg(background)=ColorIncorrect, TFSlopeMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(TEXTreply2a,trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
else
  Set(TFSlopeMsg=TEXTIncorrect,
    TFSlopeMsg(background)=ColorIncorrect, TFSlopeMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(sorry[randsorry()],trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if;
end proc:
SlopeShow:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(TFSlope="f(x)"):
Set(TFSlopeMsg=TEXTShown,
  TFSlopeMsg(background)=ColorShow, TFSlopeMsg(foreground)=ColorShowFrgd):
Set(reply=shows[randshow()],
  reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
Set(BDerivCheck(enabled)=true, BDerivCheck(background)=ColorCheckButton);
Set(BDerivShow(enabled)=true, BDerivShow(background)=ColorShowButton);
end proc:

DerivHint:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(reply=TEXTDerivHint, reply(background)=ColorHint, reply(foreground)=ColorHintFrgd):
end proc:
DerivCheck:=proc()
local userDeriv;
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

userDeriv:=Get(TFDeriv::anything, corrections, update);
if userDeriv=f(x) then
  Set(TFDerivMsg=TEXTCorrect,
    TFDerivMsg(background)=ColorCorrect, TFDerivMsg(foreground)=ColorCorrectFrgd):
  Set(reply=great[randgreat()],
    reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd):
  Set(ARunFTC(run)=true):
else
  Set(TFDerivMsg=TEXTIncorrect,
    TFDerivMsg(background)=ColorIncorrect, TFDerivMsg(foreground)=ColorIncorrectFrgd):
  Set(reply=cat(sorry[randsorry()],trys[randtry()]),
    reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd):
end if;
end proc:
DerivShow:=proc()
options `Copyright 2006-10, Philip B. Yasskin and Douglas B. Meade for WebALT.`;

Set(TFDeriv="f(x)"):
Set(TFDerivMsg=TEXTShown,
  TFDerivMsg(background)=ColorShow, TFDerivMsg(foreground)=ColorShowFrgd):
Set(reply=shows[randshow()],
  reply(background)=ColorShow, reply(foreground)=ColorShowFrgd):
end proc:

AreaDeriv:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN]( title=TEXTtitleMAIN, defaultbutton=BPlay,
[ valign=none, halign=none, inset=0, spacing=0, background=ColorBkgd,
  [ background=ColorBkgd, halign=none,
    TextBox(TEXT0a, width=80, height=2, background=ColorMessage, editable=false),
    HorizontalGlue(),
    Button(TEXTBQuit, Shutdown(), background=ColorCloseButton)
  ],
  [ valign=none, halign=none, inset=0, spacing=0, background=ColorBkgd,
    [ background=ColorBkgd, border=true, halign=none, inset=0, spacing=0,
      caption=TEXT1cap,
      [ background=ColorBkgd, halign=none, inset=0, spacing=0,
        TextBox(TEXT1a, width=20, height=1, background=ColorMessage, editable=false),
        " ",
        MathMLViewer[MMLarea](value=MathML[Export]( `A'`(x) = Limit((A(x+h)-A(x))/h, h=0) ), height=50, width=250)
      ],
      [ background=ColorBkgd, halign=none, inset=0, spacing=0,
        CheckBox[CBPlotArea](TEXTCBPlotArea, Evaluate(function="PlotIt"), background=ColorBkgd),
        HorizontalGlue(),
        TextBox(TEXT1b, width=58, height=3, background=ColorMessage, editable=false)
      ],
      [ background=ColorBkgd, halign=none, inset=0, spacing=0,
        TextBox(TEXT1c, width=73, height=2, background=ColorMessage, editable=false),
        HorizontalGlue()
      ],
      [ background=ColorBkgd, halign=none, inset=0, spacing=0,
        CheckBox[CBPlotRect](TEXTCBPlotRect, Evaluate(function="PlotIt"), background=ColorBkgd),
        HorizontalGlue(),
        TextBox(TEXT1d, width=58, height=3, background=ColorMessage, editable=false)
      ],
      [ background=ColorBkgd, halign=none, inset=0, spacing=0,
        TextBox(TEXT1e, width=73, height=1, background=ColorMessage, editable=false)
      ]
    ],
    [ background=ColorBkgd, border=true, inset=0, spacing=0,
      caption=TEXTCapAnim,
      Plotter[PFTC](d00, height=200, width=350, play=true),
      [ background=ColorBkgd,
        Button[BPlay](TEXTBPlay, onclick=SetOption(PFTC(play)=true), background=ColorPlotButton, foreground=ColorPlotButtonFrgd),
        Button[BPause](TEXTBPause, onclick=SetOption(PFTC(pause)=true), background=ColorPlotButton, foreground=ColorPlotButtonFrgd),
        Button[BStep](TEXTBStep, onclick=Action(SetOption(PFTC(pause)=true),
          SetOption(PFTC(frame_forward)=true)), background=ColorPlotButton, foreground=ColorPlotButtonFrgd)
      ],
      [ halign=none, background=ColorBkgd,
        TEXTSlower,
        Slider[SlSpeed](0..500, 250, filled=true, majorticks=50, snapticks=false, showlabels=false,
          onchange=Evaluate(function="SetSpeed"), background=ColorPlotButton, foreground=ColorPlotButtonFrgd),
        TEXTFaster
      ]
    ]
  ],
  [ valign=none, background=ColorBkgd, inset=0,
    [ valign=none, background=ColorBkgd, border=true, inset=0, spacing=0,
      caption=TEXT3cap,
      [ background=ColorBkgd, spacing=0, halign=none,
        TEXTApproximate,
        MathMLViewer[MMLDiff](value=MathML[Export]( A(x+h)-A(x) ), height=30, width=200),
        Label(" H "), # The " H " does not always work. I want an approximate equal sign, but how do I get it?
        TextField[TFDiff]("", width=20, background=ColorInput),
        HorizontalGlue(),
        Button[BDiffHint](TEXTBHint, Evaluate(function="DiffHint"), background=ColorHintButton),
        Button[BDiffCheck](TEXTBCheck, Evaluate(function="DiffCheck"), background=ColorCheckButton),
        TextField[TFDiffMsg]("", width=6, editable=false, background=ColorMessage),
        Button[BDiffShow](TEXTBShow, Evaluate(function="DiffShow"), background=ColorShowButton)
      ],
      [ background=ColorBkgd, spacing=0, halign=none,
        TEXTApproximate,
        MathMLViewer[MMLSlope](value=MathML[Export]( (A(x+h)-A(x))/h ), height=40, width=200),
        Label(" H "), # The " H " does not always work. I want an approximate equal sign, but how do I get it?
        TextField[TFSlope]("", width=20, background=ColorInput),
        HorizontalGlue(),
        Button[BSlopeHint](TEXTBHint, Evaluate(function="SlopeHint"), background=ColorHintButton),
        Button[BSlopeCheck](TEXTBCheck, Evaluate(function="SlopeCheck"), background=ColorDisable, enabled=false),
        TextField[TFSlopeMsg]("", width=6, editable=false, background=ColorMessage),
        Button[BSlopeShow](TEXTBShow, Evaluate(function="SlopeShow"), background=ColorDisable, enabled=false)
      ],
      [ background=ColorBkgd, spacing=0, halign=none,
        TEXTSo,
        MathMLViewer[MMLDeriv](value=MathML[Export](` A'`(x) = Limit((A(x+h)-A(x))/h, h=0) ), height=50, width=250),
        " = ",
        TextField[TFDeriv]("", width=20, background=ColorInput),
        HorizontalGlue(),
        Button[BDerivHint](TEXTBHint, Evaluate(function="DerivHint"), background=ColorHintButton),
        Button[BDerivCheck](TEXTBCheck, Evaluate(function="DerivCheck"), background=ColorDisable, enabled=false),
        TextField[TFDerivMsg]("", width=6, editable=false, background=ColorMessage),
        Button[BDerivShow](TEXTBShow, Evaluate(function="DerivShow"), background=ColorDisable, enabled=false)
      ]
    ]
  ],
  [ background=ColorBkgd,
    TextBox[reply](width=100, height=2, editable=false, background=ColorMessage),
    Label(Image(Logo)),
    Label(Image(LIBLogo))
  ],
  BoxColumn( halign=none, background=ColorFooter, inset=0, spacing=0,
    [ background=ColorFooter, inset=0, spacing=0,
      Label(TEXTLprogrammers, font=FontFooter),
      HorizontalGlue(),
      Label(TEXTLcopyright, font=FontFooter),
      HorizontalGlue(),
      Label(TEXTLversion, font=FontFooter)
    ],
    [ background=ColorFooter, inset=0, spacing=0,
      Label(TEXTLasstprogrammer, font=FontFooter),
      HorizontalGlue(),
      Label(GetVersion(), font=FontFooter)
    ]
  )
]),#close BoxColumn, Window,
Window[FTC]( title=TEXTtitleFTC, defaultbutton=BCloseFTC,
[ background=ColorBkgd, halign=none, 
  [ background=ColorBkgd, halign=none, 
    TEXT4a,
    HorizontalGlue(),
    Button[BCloseFTC](TEXTBClose, CloseWindow(FTC), background=ColorCloseButton)
  ],
  [ background=ColorBkgd, halign=none, 
    HorizontalGlue(),
    TextField(TEXT4b, width=25, background=ColorHint),
    HorizontalGlue()
  ],
  [ background=ColorBkgd, halign=none, 
    TextBox(TEXT4c, height=3, width=75, background=ColorHint)
  ]
]),#close BoxColumn, Window,
Action[ARunFTC](RunWindow(FTC))
): #close Maplet
Maplets[Display](AreaDeriv);