Using printlevel is a crude tool for debugging only. It's impossible to get it to display only the information that you want. Thus it is never intended for the display the output of a finished procedure.

If you have a procedure that generates plots which are not the official return value of the procedure, but you want to see them anyway, the use print in the procedure, as in

print(plots[display]( ...your exact same display command here...));

The point-data matrices can be extracted from a plot like this:

P:= implicitplot(...your exact same command...);
(M1,M2):= map2(op, -1, [plottools:-getdata(P)])[];

Now M1 and M2 will both be two-column matrices, the first for disf and the second for dispbeamf.

How about

convert(simplify(eval(diff(f(x),x)*cos(f(x)), x= RootOf(f(x),x))), D);

Use eliminate instead of solve. The second set returned is the conditions (which must be understood to be equated to 0).

You're asking for a 3D plot, yet nowhere in your command do you specify which functions are to be represented on each of the three axes.

If you want all decimal numbers to be displayed with 3 digits after the decimal point (or decimal comma, if that's what your culture uses), give the command

interface(displayprecision= 3);

This can also be set from the Tools -> Options menu.

Factoring polynomials over the rationals is a completely solved problem, whose solution has been completely implemented in Maple for a great many years, at least 17. If you mean to express the given polynomial as a sum of some small number (but greater than one) of factored polynomials, that's a different problem that's not called "factoring" strictly speaking.

If you have an example of a rational-coefficient polynomial that Maple can't completely factor, please report that as a bug, or post it here.

You can see a plaintext form of your most-recent output by the command lprint(%).

Do you really need to use package MTM for this? It seems to have trouble deciding which variable the limit is taken with respect to (although that is obvious to us). The following works fine:

restart;
limit(BesselY(1, -I*r*sqrt(s)), r= infinity) assuming s > 0;

The command add does not require that all the variables have numeric values; all that's required is that the lower and upper limits of summation have numeric values. In your case, m doesn't have a numeric value.

No, it's not true: The sign of x has nothing to do with it. However, if both a(x) > 0 and b(x) > 0, then arctan(a(x), b(x)) = arctan(a(x)/b(x)). It's the sign of the functions' values that matter, not the sign of the functions' arguments.

Your code is definitely stored in an ordinary file and not in some special file system maintained by Maple. You can learn (or change) the directory (aka folder) that the file is stored in with the command currentdir().

One way:

plots:-odeplot(
   sol, (r*~[cos, sin])(theta), theta= 0..2*Pi,
   axiscoordinates= polar
);

It can be done with a single solve command like this:

f:= x-> 10000/(1+30762*0.478^x)+5:
solve({D(f)(x) = M, (D@@2)(f)(x) = 0, (D@@3)(f)(x) < 0});

     {M = 1845.361366, x = 14.00001597}

The inequality condition is just to verify that it's a maximum.

Yes, it seems that that button becomes inactive, as well as the corresponding menu entry and key shortcut. But you can still single-step through the commands in another worksheet by pressing Enter. The second worksheet should be opened before you begin executing the first.