The first error message says "Warning, expecting only range variable x1 in expression 29239.76608*Ex*x1+794956140.3-29239.76608*Ma-131578.9474*Ey to be plotted but found names [Ex, Ey, Ma]". So you have not given numerical values to Ma, Ex, and Ey. The thing you are trying to plot is

29239.76608*Ex*x1 + 7.949561403*10^8 - 29239.76608*Ma - 131578.9474*Ey

but it can have only the name x1 in. You can try, say 

and you do get a plot, but I don't know what values of these parameters would be sensible.

Download solve.mw

I don't think you can expect sum to give an analytical result, but you can use add to get a numerical result for summing up a large but finite number of terms. (Of course you can use ":" before the evalf to suppress the fraction.) There are probably ways of speeding this up if you want more terms and are only interested in a floating answer.

Download igcd.mw

I usually use a colon at the end of an assignment statement storing a plot in a variable, then display it:

plt0 := implicitplot3d(pln, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, style = patchnogrid, transparency = 0.6):
display(plt0);

What you see with a semicolon in the first line has changed over various versions (plot structure, miniplot, full plot); I didn't check here. But also I would store the plot and not the display of the plot.

That format is hardcoded somewhere hard to find. Here's a hack that takes the existing output and substitutes different strings. Here I use the 5.1f format to get one decimal place.

VennHack.mw

You can collect your Usol values in a table by indexing them. See in red.

ode.mw

0 means an exact result. In general in Maple, numbers with a decimal point are approximate (floats) and without are exact. So if the numbers in your guesses were entered as, e.g., 3. instead of 3 or with an e (1e3 instead of 1000), then you will get an approximate result which will be displayed with a decimal point. evalf() will convert an exact expression to an approximate one ("f" for float).

Minpoly looks for the monic polynomial of least degree that has the expression as a root.

Download simplify_symbolic_numbers.mw

Download odetest_challange_may_15_2025.mw

Your lines

P3 = (5/2)*x^3-(3/2)*x;
R3 = GM3*(rho1/rho2)^3*P3/rho2;

should have := rather than = 

This is fixed in Maple 2025

Download mellin.mw

It's not clear to me what you mean by simple elements. Normal will simplify the rational function in F11 as below, but the answer is just the reciprocal of your original polynomial. In future please upload your worksheet using the green up-arrow in the Mapleprimes editor so we don't have to retype and can diagnose more subtle issues such as why the parfrac did not work.

Download mod11.mw

collect is really only for polynomials and here the powers are not integer (though it works with a few other things like diff or exp). So you can do it by subs and then collect (the expand you had is essential).

 collect_term.mw

If you don't take the sqrt of the ode (which has consequences for the validity of the assumptions on signs), then many of the odetest's give zero. I didn't check them all.

17-ode.mw

In this case there is a simple solution. But in principle, your question doesn't have a clear answer - what do you want to do with terms that only have only diff(G(xi),xi) for example - do you want to write that as (diff(G(xi),xi)/G(xi))*G(xi) and count it?

Download collect-coe.mw