@Markiyan Hirnyk 

That's an astounding performance by DirectSearch:-GlobalOptima. What's the significance of the 2921? I thought that it was the number of objective function evaluations. But if there were only 2921 evaluations, what was it doing for several hours?

@Markiyan Hirnyk 

I don't understand what point you're trying to make. Your plot and computation simply confirm what I said.

@Markiyan Hirnyk 

Maple can complete the integration even without knowing eta(t) if you follow the steps in my Answer below. Since the integration is wrt x, the functions of t can be factored out.

@reinhardsiegfried 

Oh, yes, you can use any strings whatsoever as the labels of the legend. There is no need to include the algebraic expressions such as x, x^2, or x^3.

@kegj 

So there really is no course website that you could direct me to? That is suprising. That makes it hard for me to help you. Could you email me (privately) photographs of the syallabus and exercises? If so, I'll send you my email address.

What data structures have you covered? Lists, tables, arrays, stacks, queues? Perhaps even trees and graphs?

As to control flow, fortunately there's only a handful of statements that you need to know. Study their help pages thoroughly. They are
for...while...do
if...then...elif...else
proc 
return 
break
next
and perhaps try...catch...finally and module.

(return only makes sense inside a proc. break and next only make sense in a do loop.)

By the way, I think that you are being too harsh on Rouben. I believe that his advice was well intentioned but overly idealistic. As a professional tutor who helps students study for exams, I know that studying for the exam is essential for the vast majority of American college science courses.

@tomleslie 

Most of the old-timers here on MaplePrimes are inured to bug reports: We've seen literally thousands of them. Just because we don't get emotionally worked up over them doesn't mean that we find them acceptable. So, most bug-related discussion here is about finding practical solutions (aka workarounds) to your problems that can be implemented immediately, before the bug is fixed.

You should use the green uparrow to upload your worksheet. That is much more useful than pictures. The green uparrow is the last tool on the second row of the toolbar in the MaplePrimes editor.

My first guess is that the fsolve is being executed, but that it cannot find any real solutions. You can determine if this is the case by putting the fsolve command in its own execution group, or by using 1D math.

@Preben Alsholm 

The add(x, x= myMat[5, 1..-1]) worked in Maple 16.

It's a real shame to need to refer to the 40 in order to get this to work.

@Kitonum 

A single-line verify that works:

verify(abs(x), sqrt(x^2), simplify) assuming x::real;

     true

Why do you consider this situation to be a problem? That's just the way Maple works. There's one GUI process and at least one "kernel" or "server" or "evaluating" process.

@Rouben Rostamian  

Your plotting solution is remarkably simple. Note that if you change the positive `if` target from [H2,y,z] to either [x,y,H1] or [H2,y,H1], it doesn't substantially change the shape of the plot. However, the grid lines on the vertical surface are changed.

@Kitonum Your counting algorithm does not allow for nonpositive _Z6 and _Z7.

This help page may be useful to you: ?worksheet,managing,exportHTML

Regarding converting a whole worksheet to MathML: A worksheet can (and usually does) have content that is not valid expressions. How is that content supposed to translated to MathML?

@Kitonum Yes, I like it better than what I wrote for the first matrix.

If you could direct me to a course website where I could see a syllabus and/or some sample exercises, I may be able to advise you.