@nm 

Why there are no better debugging tools? I suppose that Maplesoft has better debugging tools for internal use. The fact that the old tool is still available, but no better one, could be because Maplesoft want to make it difficult for other companies to reengineer Maple algorithms. The openess of Maple (which I appreciate) might be one of the reasons why Maple lost its leading position. 
I remember a time when Mathematica was inferior in many aspects. Maybe they copied to catch-up. 

I am not using the debugger very often but sometimes I use showstat on procedures to be debugged in a separate worksheet for better oversight without the need to scroll.

@Sim123 

What you are showing is new. I would also contact support.

I would keep it. Several users had firewall issues recently. 

In my case my IP was blocked but I could access other Maplesoft urls. 

It would be helpfull to post a screenshot of the firewall message.

@acer 

Yes, I misunderstood.

The 1D plaintext came from converting 2D Input to 1D with the intend to see what was behind this error message

Concering the use of atomic, I either do something wrong or my setting performs differently.

I might come back here but need some time for tests.

As always, thank you for your time!

@acer

I do not want to change the default setting as you have shown with:

Typesetting:-Settings(useprime = false)

To make sure that I understand your answer correctly. By single right quotes you do not mean

The key (on my keyboard) next to the tilde key "~" (for which I have to do Alt+tilde followed by spacebar) shows a single right quote but it does not print in Maple. In MS-Word for example it prints; see here: "´". I can paste this symbol from Word to Maple and make it work in Math-1D but not in Math-2D

Using Alt+´ followed by spacebar would indeed be easier than the keyboard acrobatics I have mentionned above. Right now I cannot make single right quotes appear and work in Math-2D.

By the way: Omitting the name quotes leads to an unpleasant overlap (yellow below) in the input and the output

whereas namequotes are visible in the input when I use atomic variables from the favorite palette.

With right single quotes from the favorites it looks better. That is already an improvement.

@GunnerMunk 

I cannot reproduce the results with capital M. Could you send a Maple file (with the green arrow) and tell us if you have used any special unit settings (like with(Units[Simple]))

From ?solve,details

The solve command returns all solutions for polynomial equations. In general for transcendental equations, the solve command returns only one solution, but does not set _SolutionsMayBeLost to true. To force the solve command to return the entire set of solutions for all inverse transcendental functions, provide the solve option allsolutions = true

I would have expected one solution without allsolutions.

This one also does not return a solution

solve(sin(x)/x)

@janhardo 

Expr := Int(1 / (sqrt(-alpha*l^2 + 1) * %sqrt(-alpha*l^2 * (x + 1)/2 + 1)), alpha = 0 .. z);
Expr = value(Expr);

All by hand...not very practical in larger expressions
Thank you

@janhardo 

Yes Il-subs is the normal form I would like to achieve. 

So far I could only achieve it by hand and making sqrt inert to prevent automatic simplification

@nm 

I was about to ask if I am the only one in need of this functionality. Since MMA has it, there must be a need.
Thanks for checking

@janhardo

The first one in this particular example. It is closer to the normalized form of first incomplete elliptic integral.

Only for information:
Ideally after further manipulation I would like the get the following displayed

However automatic simplification kicks in and prevents this by automatically factoring out 2.

@Kitonum 

That looks promissing! A magic wand command (that I was hoping for but apparently does not exist) could apply the above applyop command over all subexpression provided that a listlist of all branches of subexpressions of the "main expression" (the equation in my example) exsisted.

@Kitonum 

I was not aware of these commands. Reading the top level description of the help page I would not have guessed that they work also on square roots of polynomials. Unfortunately they are only effective on such objects.

In my original post I was looking for a command that "brushes" over a larger expression and does the extraction on every occurence of a square root that allows for such an operation. I have added an example in which the commands you provided are not effective on either side of an equation. 

I have tried to make a function out of your commands and somehow "map" it over all the subexpressions. This did not work well but maybe someone can provide a highlevel command that does it. That is where I stopped with partial success on the rhs

extract_prim := x -> content(x)*primpart(x);
applyop(extract_prim, {i $ (i = 1 .. nops(rhs(expr)))}, rhs(expr));

Too complicated IMO.

Anyway, thank you for the answer. I still hope for something better but I have doubts now. 

@sand15 @nm

It seems that the convention Maple uses (sin(phi) instead of the amplitude phi for the first argument of EllipticE) is the trouble maker when doing the integration. Without allsolutions a wrapped representation of the integral is produced. This is not what we expect for the integral. The need of using allsolutions is unfortunate to get the expected solution. 

plot(int((1 + sin(x)^2)^(1/2), x = 0 .. x, allsolutions),x=0..10);

Also the piecewise expression behind the plot is very complicated. There might be other advantages for this convention but here I do not see any. Who knows... 
I am wondering whether some of the struggles I have would not happen on other CAS platforms. 
IMO, Maple should not have returned the wrapped expression in the first place or at least give a hint to the unprepared user about the restricted domain/wrapped results (the definition section of FunctionAdvisor(EllipticE) is not helpfull in this respect) or the use of allsolutions. 

@sand15 

X0, Y0, X and Y are column vectors.

The first error message is generaded in Step 1 here

Download Compare_outputs_2015_your_version_reply.mw