@acer 

Using Maple 18, the plotsetup command is not working for me. The plot still goes to the screen, and the file is never created; nor is there any error message about not being able to create the file. I even tried putting a Threads:-Sleep(2) on each side of the plotsetup. Do you have any idea what's going wrong?

Update: Problem solved! I needed to put the restart in a separate execution group. This shows that the help file ?restart is not quite correct. It says (in the eighth paragraph of Description) that the restart should be on a separate line. Actually, it needs to be in a separate execution group. I've long suspected this, and now there's proof.

The Threads:-Sleep after the plotsetup is also necessary.

There's no way to do that with the text treated simply as plaintext. But if the text (or any other image) were in a JPEG file, then it'd be possible.

Update: As Acer shows below, getting the text into a file in a graphics format is pretty easy.

For what it's worth, I've reduced the task to some simpler-looking expressions and generalized the integral. Let

H:= hypergeom([m,-m], [m+1], 1/2);
G:= 2^(-1-m)*(sqrt(Pi)*GAMMA(m)*m/GAMMA(m+1/2) + 1);
J:= Int(abs(x-(1-x^n)^(1/n)), x= 0..1);

I've proved that if H = G for m > 0, then J = 1/2 for n > 0. Graphical/numerical evidence strongly supports the equalities.

@MDD

If Acer's way isn't generalizable for your purpose, then you need to show an example where it won't work for your purpose and what the desired coefficient matrix for that example is. 

Note that any command that works for an individual polynomial can be mapped over a Matrix of polynomials.

@reinhardsiegfried 

I got one t^3 term and O(t^4). But I don't know how you corrected the two syntax errors in your p1. You may have corrected differently than me. In your latest example, the expanded polynomial does not have any terms of degree 3 or less in t. That's why it shows just O(t^4). If you want to include terms of degree 4 in t, use 

series(expand(p1), t, 5);

@hopereza 

The problem is not with map. As you yourself show in the worksheet, the same error ensues when you try to apply int to an individual array element. What you have found is a bug in the symbolic integration of some functions of the form exp(a*x)*R(x) where R(x) is a rational function. You can get around this by forcing numeric rather than symbolic integration. You do this by replacing

map(int, ...);

with

map(evalf @ IntegrationTools:-Expand @ Int, ...);

Note the capital I in Int. Since you have so many floating-point coefficients, you may improve accuracy if you replace the other, currently working, integration likewise. The error control in Maple's numeric integration is very good.

I see that you tried to use evalm in your code. This command has no use in modern Maple. It is only present so that legacy code continues to work. Please don't ever use it.

@hopereza Please post a worksheet where it doesn't work. 

@digerdiga 

plot(Product(1 - q^(5*k+1), k= 0..infinity), q= -1..1);

@Markiyan Hirnyk It seems that `#mn(01)` prettyprints the same as `#mn("01")`, but it is easier to type.

@itsme 

It's a good solution, but it should be noted that

1. The double underscore produces a result that prettyprints the same as an indexed name but which acts programmatically like a symbol, an unindexed name.

2. mu__01 prettyprints the same as mu[`01`], with the 01 in italics. mu[`#mn(01)`] prints with the 01 normal, upright.

@hopereza 

Hmm, the tilde is not working in your worksheet. I don't understand why yet. But I tried this in your worksheet, and it definitely works:

map(int, Phi^%T*f, x= 0..1);

@Markiyan Hirnyk I converted your Reply to an Answer and gave it a vote up. I think that your solution is better than mine.

@Rouben Rostamian  ScalarMultiply multiplies a Matrix or Vector (its first argument) by a scalar (its second argument) according to ?ScalarMultiply.

@itsme In Maple 18, I find no command named Grid:-Set. There is a Grid:-Setup, but this does not seem to have anything to do with copying memory.

@smith_alpha 

C:= ImportMatrix(
     "C:/Users/Carl/Desktop/Matrix.txt",
     skiplines= 1, source= delimited, delimiter= " ", transpose
);