By solving for where the arguments of the three logarithms are positive, we can see that the answer returned by solve is the domain of the function, not where the function is positive. So this is a bug. After that, I solved it by the plot and fsolve method, but Thomas Richard posted it first.

@Joe Riel I believe that Acer, in this thread, applied the same asolve to the OP's function but on the domain 0..100 and showed that it didn't get all the roots.

The procedure asolve seems to be coded to include the possibility that fsolve could return more than one root per call. When does that happen for a nonpolynomial? (For a polynomial, asolve is unnecessary because fsolve returns all real roots.)

@eclark Nice to see that you're still in the Maple community.

@Dmitry You asked:

Why does Maple need to make up a new variable?

It is always proper for the variable of integration (or any other bound variable) to be a variable that does not otherwise appear in the problem.

Why the obtained solution is presented in the integral form even when the initial conditions were supplied?

I can't say for sure without seeing the problem. Please post it. One possible reason is that the answer would be significantly more complicated if the integral were evaluated. Another is that it may be necessary to make assumptions on the parameters in order to evaluate the integral.

@spradlig This is an intermittent bug that has been discussed on MaplePrimes before. I can't remember the solution. I am going to guess that it can be solved by

plotsetup(inline);

If you actually want text-based plots, you can get them with

plotsetup(char);

@nm Yes, the rendering of those images is hideous and difficult to read even at a high zoom setting. It is ironic that the topic is signal processing.

@Joe Riel I would only trust that method if I knew how many roots there were. I have had cases where the fsolve starts to return unevaluated even though there are still roots to be found.

It looks like a right angle to me also. Get a ruler and measure the grid spacing.

@Kitonum The source of the bug is that you forgot to make x and y local.

@Kitonum I also get true for Markiyan's example. This must have something to do with a version change in Maple.

@brian bovril 

On Windows, create a plain text file named maple.ini and put it in C:/Program Files/Maple 17/Users. You can put any Maple commands in this file. What I have is

Digits:= 15;
kernelopts(opaquemodules= false);
interface(rtablesize= 30);
interface(prompt= "");
libname:= libname, "C:/Maple_packages";

@Shanobadur 

Detecting repeated vertices is easy:

SignedArea := proc(Pts::list([algebraic,algebraic]))
local i, P:= [Pts[], Pts[1]];
     if nops(Pts) <> nops({Pts[]}) then return 0 end if;
     add(P[i][1]*P[i+1][2]-P[i+1][1]*P[i][2], i=1..nops(Pts))/2;
end proc:

@nm The operands of [[1,2],[3,4]] are [1,2] and [3,4]. So map(igcd, [[1,2],[3,4]]) is equivalent to [igcd([1,2]), igcd([3,4])]. This doesn't work because igcd doesn't take a list as an argument. You are confusing extracting the operands of [[1,2],[3,4]] with extracting the operands of [1,2] and [3,4].

Is that sufficient explanation?

@nm In ~set, it is a completely different use of ~ than an elementwise operator. The ~set is a coercion procedure (see ?coercion ). It is used to force a conversion from other data types into a set. IfT is any type name, then you can write a procedure ~T that converts other types to T. Then you can use ~T as a type in a procedure's parameter declarations. When that procedure is passed an argument that is not of type T, then procedure ~T is applied to that argument.

Is that sufficient explanation?

@Markiyan Hirnyk What if the sample was of size 30 or larger? If we have a large (possibly infinite) stream of selections from combinat:-choose(8,5), how can we decide whether the selections are done uniformly at random? Such a process must be used to test the randomness of a lotto machine.