Instead of a TextArea, you could also use a Slider, something like this:

G2:= proc()
   local s,t;
   s:= time();
   while time() < s + 20 do
     t:= time();
     while time() < t+1 do end do:
     Maplets:-Tools:-Set(SL1(value)=round(t+1-s));
   end do;
 end;
with(Maplets[Elements]):
 maplet2 := Maplet([[
    Slider['SL1'](0..20,showticks,'majorticks'=10, 'minorticks'=1),
    Button("Go", Action(Evaluate('function'='G2()'))),
    Button("Done", Shutdown())
 ]]):
 Maplets[Display](maplet2);

Unfortunately, the new components introduced in Maple 12, such as Volume Gauge and Rotary Gauge, are not in the Maplets package.

I know very little about flash, but if you can run external programs from it you should be able to call command-line Maple with a text file as input, telling Maple to write its output to another text file, and use that as data for the animation.  The command line to call Maple on a Windows system might be something like

"c:\Program Files\Maple 12\bin.win\cmaple" -q code.mpl

where code.mpl contains the code you want Maple to run.

The alternative might be to use OpenMaple.  That has API's for C, Java and Visual Basic: I don't know if any of those would be useful to you.

I know very little about flash, but if you can run external programs from it you should be able to call command-line Maple with a text file as input, telling Maple to write its output to another text file, and use that as data for the animation.  The command line to call Maple on a Windows system might be something like

"c:\Program Files\Maple 12\bin.win\cmaple" -q code.mpl

where code.mpl contains the code you want Maple to run.

The alternative might be to use OpenMaple.  That has API's for C, Java and Visual Basic: I don't know if any of those would be useful to you.

I can confirm: it works in Maple 11.02, not in 12.0 (in this case both under Windows XP). 

I suspect the change is due to efforts to address the performance issues that have plagued the Standard GUI ever since its introduction.  One way to improve performance is to prevent unnecessary redrawing.  Only in this case the redrawing was necessary.

I can confirm: it works in Maple 11.02, not in 12.0 (in this case both under Windows XP). 

I suspect the change is due to efforts to address the performance issues that have plagued the Standard GUI ever since its introduction.  One way to improve performance is to prevent unnecessary redrawing.  Only in this case the redrawing was necessary.

Hmmm.  this didn't work for me: the TextArea stayed blank until the very end, then suddenly filled with a's.  I tried it under both Windows Vista and Ubuntu Linux.

Hmmm.  this didn't work for me: the TextArea stayed blank until the very end, then suddenly filled with a's.  I tried it under both Windows Vista and Ubuntu Linux.

ztrans(f(t),t,z) = sum(f(n)/z^n, n=0..infinity)

so if f(n) is undefined or infinite for any nonnegative integer n, the Z transform should be undefined.

Dirac(0) is undefined.  The Delta(n) used in the z transform literature is 1 at n=0.

Actually it doesn't.
First of all, because of adaptive plotting, there will be more than 100 points, unless you use the option adaptive=false.
Second, the points (except at the start and end) are slightly, somewhat randomly, displaced from equal spacing.  The resulting points are floats, which when converted to rationals have rather large denominators.

Here is a reasonable approximation to the graph.

> plots[pointplot]([seq(seq([a/b,1/b],
      a=select((t->igcd(t,b)=1), [$1..b])),b=1..200)],
    symbolsize=4,colour=red);

What do you mean by "it"?  The difference of two cubes factors:

> factor(a^3 - b^3);

(a-b)*(a^2+a*b+b^2)

Or is "it" x, which is 1 + a^3 - b^3?  As a polynomial, this is irreducible:

> factor(1 + a^3 - b^3);

1+a^3-b^3

If a and b are supposed to be integers, then the fact that x-1 = a^3 - b^3 does not particularly help in factoring x, which may happen to be prime (e.g. for a=7, b=3).

Using c for cos(x) and s for sin(x), with the algebraic relation c^2 + s^2 - 1 = 0, we eliminate c:

> F:= c - x*s + 1;
  factor(resultant(F, c^2 + s^2 - 1, c));  

s*(x^2*s+s-2*x)

So any solution of f(x)=0 must have either sin(x) = 0 or g(x) = 0.  The solutions of sin(x)=0 for which cos(x) = -1 are of course solutions of your equation. 
On the other hand, a solution of g(x) = 0 is not necessarily a solution of your equation, because cos(x) might be the wrong square root of 1-sin(x)^2.  It has been noticed here before that Maple sometimes includes spurious solutions, e.g. see www.mapleprimes.com/forum/interpret2symbolicsolvesolutionswhenonly1numericalsolutionexists

What legend?

Maple 12 Classic (but Standard would work too):

> with(Student[Calculus1]):
  eval(ApproximateInt(x^2, x=0..1, output=plot),LEGEND=NULL);

The "Partitions: 10" is not a legend.

What legend?

Maple 12 Classic (but Standard would work too):

> with(Student[Calculus1]):
  eval(ApproximateInt(x^2, x=0..1, output=plot),LEGEND=NULL);

The "Partitions: 10" is not a legend.

According to the OEIS entry, there is a "closed form", if you count 2F1 hypergeometric functions:

p(n) = hypergeom([2-n, n+1], [2], -1)