@Kitonum This can be improved by not requiring a priori knowledge of the range of exponents:

add(coeff(P(z),z,n)*z^(``(n)), n= ldegree(P(z),z)..degree(P(z),z));

@Joe Riel That's great, Joe. You should put that on the Applications Center.

So, it is possible to read from the mouse in Maple.

This is an integral equation of a type that Maple does not know how to solve. So, you'll need to transform the equation somehow.

How many points are there for which f(x)=0? Do you mean that D(f)(a) = -K where a is the first value to the right of 0 such that f(a)=0 and that you want the boundaries for the BVP to be 0 and a?

@dungct What do you want it to return other than zero?

@sarunas 

evalf(arctan(519/520));
                       0.784435699787033
evalf(convert(%, degrees));
                    44.9448548971883 degrees

@bernie Then you need a zip of aribitrary arity, like this:

N_aryZip:= proc(F, LL::seq(list), $)
local l,k, L:= [LL], n:= nops(L[1]);
     [seq(F(seq(l[k], l= L)), k= 1..n)]
end proc;

@Adri van der Meer These (the original equations, not the Maple code) are partial differential equations.

@Markiyan Hirnyk I was wrong, and I did not understand the question.

@abbeykabir The code is separating the real (Re) and imaginary (Im) parts of the roots. The real part is used as the x-coordinate of a point in the plot, and the imaginary part is used as the y-coordinate. The code (L-> [Re,Im]~(L)) ~ ([R1,R2]) is equivalent to the following:

F:= z-> [Re(z), Im(z)]:
[map(F, R1), map(F, R2)]:

As for a name for the plot, I'd call it a "plot of points in the complex plane".

@bernie You're right---the modification to noninteger values wouldn't work.

So, how about this?

Alist:= [seq(i, i= 1..10, 0.5)];
Xlist:= X1 ~ (Alist);
Flist:= zip(F, Xlist, Alist);

That will work no matter how the Alist is constructed.

@maplelearner I think that as long as the lower limit is greater than 0 and the upper limit is less than infinity, the evalf will work.

I think that the integral at infinity does not exist. Applying asympt to the inner integrand gives a leading term that is O(1/x^2). So the inner integral is O(1/y). So the outer integrand is O(1).

@acer A slight improvement: Increase numpoints for the default-method (rkf45) plot. There is obvious polygonizing for the first few steps unless you set numpoints to about 2^9 or higher.

@acer I note that the original post is 3-1/2 years old.

@Sujaan Kunalan The default method is Runge Kutta Fehlberg, abbreviated rkf45.