@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.

@reinhardsiegfried Could you provide details of what you're talking about with 'f1'=x?

@Rouben Rostamian  

In Standard, you can't easily get the legend vertically stacked on the bottom, but you can get it vertically stacked on the side, like this:

plot([x,x^2,x^3], x= -1..1, legend= [x,x^2,x^3], legendstyle= [location= right]);

You can fake vertical stacking on the bottom by making the labels extra long by padding with blanks:

plot([x,x^2,x^3], x= -1..1, legend= map2(nprintf, cat("%a"," "$40), [x,x^2,x^3]));

@reinhardsiegfried 

There are two things that you can do to an Answer: Give it a thumbs up, and select it as the best Answer to your Question. These actions are independent: You can do neither, either, or both.

Please check and confirm your formula. The following part looks highly suspicious to me:

(K1! * K2)!

I suspect that you mean (K1! * K2!).

@nidojan That is not a parametric plot; that is two separate plots. The OP's code as presented in the Question above is already the correct code to produce a parametric plot; there are no more brackets needed. If the OP is still receiving an error message, it is due to some hidden issue such as an invisible control character in the code.

Extracting just the essence of Markiyan's Answer (because I find it hard to read with all the extra information), we have simply

plot(x^2);
ExcelTools:-Export(op([1,1], %), "plot.xls");

What is the point of using Grid:-Seq (or even seq) for a sequence of length 1?

Where do you get the error message? When you call dsolve or when you're filling the Array using Grid:-Seq?

You've been on MaplePrimes for a year and a half, and you've asked 24 previous questions, most of which have been answered, and most of which have been about differential equations. So, can't you even attempt to solve this problem? Your attached worksheet merely contains a statement of the problem.