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.

I think that this way is simpler, and it's clear why it works if you know the simple formula for the implicit derivative: dy/dx = -(dH/dx)/(dH/dy):

H:= (1.25*y - sqrt(abs(x)))^2 + x^2 - 1:
solve({H, diff(H,x)}, {x,y}): #Find the local maxima.
solve({eval(H, x=0)}, {y}): #Find the y-intercepts.

It works just as well if you replace 1.25 by 5/4 (as an exact fraction).

If I may assume that X and x are positive integers, then all that you need is this:

scm:= (X::posint, x::posint)-> cat(0 $ max(0, length(X) - length(x)), x):
#Example (avoids need of global variable):
xx:= scm(39,7);

Edit: I changed ilog10 to length because ilog10 will be off by 1 when its argument is a perfect power of 10.

I still see the spam button. Indeed, I deleted some spam this morning.

The concept of PDF only applies to continuous distributions. At least that's the way that it is in Maple. You have what Maple calls an EmpiricalDistribution. Do like this:

Dist1:= Statistics:-Distribution(EmpiricalDistribution([0, 0.1], 'probabilities'= [0.3, 0.7]));

Now Mean, etc., will work as you expect. And yes, you can add random variables from different "discrete point distributions" as defined above, and then compute the Mean, etc. You can plot the ProbabilityFunction; as I said, the term PDF is not used for these.