Perhaps you can use implicitdiff:

implicitdiff(eq,t,Cs);

It looks a little messy, but if you can get a handle on its sign, you question is answered.

Look under Tools, Options

then you will see "Auto save every"

Set it to 12 billion years.

You could try this:

A:=R/(1+exp(-2*(h-s)));

a:=A/(exp(h-s));

expand(1/a);

simplify(%);

1/%;

It would so nice if in a case like this, we could use LaTeX:

\overrightarrow{\dot{B}}

It's so simple and so standard. But we get stuck with mathml and bizarre sequences of left and right mouse clicks mixed in with palatte selections.

You might find it useful to try an indefinite integral instead of a definite integral:

int(1/sqrt(1-k^2*sin(s)^2),s);simplify(%,trig);radsimp(%);

This seems fairly clean and unrestricted.
 

I think you want this syntax:

pdsolve(-a*u(t,x)+diff(u(t,x),t)+(c^2)*b*(1/t)*((ln(2*T/t))^(-b-1))*diff(u(t,x),x,x)=0,u(t,x));

Note that log is ln, and there are no square brackets.

One should not have high expectations for "identify." Clearly it should only act as a "suggestion."

For example,

identify(0.999);

returns 1.

Many of us have struggled to teach the structure of the real number line to undergraduates, and are  constantly frustrated by the student who knows that 0.999 is not equal to 1, but clings tightly to the idea  that 0.999(repeating) is something ever so slightly less than 1.

I am very careful to not use the "identify" command when I teach Calculus, although math majors in Analysis can appreciate the command.

Having said this, the construction

int(f(x),x=a..b) so often returns the wrong numerical value  that you start to think that

identify(evalf(Int(f(x),x=a..b)));

is more reliable! 

I tried a few things and did not find a good solution to your first problem.

Maybe you could not require html. Then you could simply use

$W0=maple("seq(ln(2*3^i),i=0..3) ");

and then in the field for the question text simply use

$W0...

It's not quite as beautiful, but pretty darn good.

Blank spaces in MapleTA are a real curse. Look at this discussion:

www.mapleprimes.com/forum/inequality-problem-with-mapleta

The first thing to ask:

Have you tried "File..Export As?"

The answer to your primary question might be this simple.

For your second question: first try to select the ouput, right-click to copy, and then paste into something like Word or Paint. This is not exactly programmatic and will lead to carpal tunnel in a few years. So look at the help screen for "plotsetup".

One thing to try is this:

If the file is named

"file.txt"  then try renaming it "file.mw" or maybe "file.mws". Next try to open it with Maple like any other mw file.

I often see students change the extension of their Maple files to .txt because our email system blocks files with extension .mw. They email the file with the txt extension, save it, then change the name back to mw.

When I use Maple 9.5, I get a solution in terms of RootOf. This might be a good place to start. I won't post it here since it is long.

Maple10, 11 and 12 all choke.

> _EnvAllSolutions := true;

 solve(((1/24)*sqrt(1/11*(819+210*sqrt(5)-126*sqrt(11)-90*sqrt(55)))*cos(sqrt(2/5*(7-2*sqrt(11)))*t*tau/h)+(1/8)*sqrt(1/33*(273+70*sqrt(5)+42*sqrt(11)+30*sqrt(55)))*cos(sqrt(2/5*(7+2*sqrt(11)))*t*tau/h))^2+(-(1/8)*sqrt(1/11*(91+39*sqrt(5)-2*sqrt(22*(47+21*sqrt(5)))))*sin(sqrt(2/5*(7-2*sqrt(11)))*t*tau/h)+(1/8)*sqrt(1/11*(91+39*sqrt(5)+2*sqrt(22*(47+21*sqrt(5)))))*sin(sqrt(2/5*(7+2*sqrt(11)))*t*tau/h))^2 = 1,t);

Since you have already created a list of 5 intervals, maybe you should leave out the option bins=5. It seems to confuse things.

Below might be close to what you are looking for. I'm not sure what you want to do with the gaps between your intervals. This shows up in the graph.

What do you mean by a "Spreadsheet Function?" Maybe an integrated (summed) version of f?

> with(Statistics):with(ListTools):

A:= <10.1, 10.6, 10.9, 10.0, 10.4, 10.5, 9.7, 10.5, 10.4, 10.1, 10.8, 9.2, 10.2, 10.3, 10.5, 9.2, 10.2, 10.5, 9.4, 10.2, 9.6, 10.2, 9.7, 10.2, 10.8, 9.9, 10.5, 10.6, 9.8, 10.7, 11.2, 10.8, 9.0, 10.0, 10.5, 10.4, 11.4,10.4, 10.1, 10.4>;

L:=[9.0..9.5,9.6..10.0, 10.1..10.5, 10.6..11.0, 11.1..11.5];

T:=TallyInto(A,L);
f:=unapply
    (piecewise(x<9.0 or x>11.5,0,
      op(Flatten([seq([(x<=op(2,L[i]) and x>op(1,L[i]),rhs(T[i]))],i=1..5)])))
   ,x);

f(x);

f(11);

plot(f(x),x=8..11.5,filled=true,color=gray);
 

If you are trying to find a way to set up the computation, then it seems as if others have answered your question many times over. What is lacking?

We all know that "plot" is numeric. But "int" is symbolic, and we all understand this distinction.

Any calculus teacher who sees

int(f(t),t=t..0)

instinctively gets nervous, because it appears that the student does distinguish between an unbound variable and a bound variable. This distinction  is a learning milestone.

Mathematicians bought into Maple because it seemed that Maple understood these nuances.

Now if you define g:=t->t,

then we are all OK with int(f(t),t=g(t)..h(t)).

But int(f(t),t=t..h(t)) is nervous.

I guess you are trying to micro-manage of typesetting of expressions with Maple. Lots of us want to do the same.

This is where one should use LaTeX. My dream is that someday, Maple will allow the user to enter LaTeX code for an expression and have that rendered in Maple, without the curse of automatic simplification.

Matlab allows this.