Any one has a trick to show in Maple that  x + sqrt(-2 + 2*sqrt(4*x^2 + 1))*sqrt(2 + 2*sqrt(4*x^2 + 1))/4; is zero for x<=0?

I'd like to get similar simplication as this below but in Maple, But everything I tried so far did not work. I am sure there is a way in Maple, but have not found it yet.

Below is the Maple worksheet

Download show_it_is_zero.mw

I use Int to show some step before evaluating it to become normal int

I'd like to show the following when the integrand is one:

But Int(x) does not work, and Int(,x) gives syntax error. So only choice is to use Int(1,x) which does not look as nice as the above

Is there a trick to use? i.e. when the integrand is one, I want to display it as the first image and not as the second image. This is just to make the Latex look a little nicer only.

I tried few things, but nothing worked so far, as Int needs something there where I want the empty spot to be (There is actually 1 there ofcourse, but I do not want to show the 1).

May be we need a Latex settings for this?  Or interface setting?

Maple 2022.1

Given

restart;
eq:=A=(1/2+x+y)^(3);
the_rhs:=solve(eq,A);

I asked solve to solve the above equation for A, expecting to get back (1/2+x+y)^(3), but it returns instead this

I looked at solve options, and tried number of them, but no change. I was looking for option to tell Maple not to simplify as it solves.

I also tried to see if the solution returned can be put back to the original form, and could not so far find a way, tried simplify and some options. But I did not try every possible method as there are do many.

Compare to Mathematica, which keeps the solution the same, as what one would expect. I see no reason to change it

ClearAll[A,x,y]
eq=A==(1/2+x+y)^3
Solve[eq,A]

The reason I am asking, is that it now makes parsing a little harder as I am looking for something in the form (expression)^power   as the solution.  i.e. the type to be `^`.    Now the type shows up as `*` because Maple for some reason changed it. 

It will easier if Maple did not do that, or if there is a way to change the expression back to the way it was. If all this fails, I have to just make the parsing handle this extra case form if needed.

Any suggestions?

Maple 2022.1

Update

Found a way after lots of trials and errors

simplify(the_rhs,[power,symbolic]);

But it would have been better if Maple did not do the simplification in the first place. But I could not find an option to tell it to do that while solving.

Maple 2022.1 on windows 10

restart;
w:=y-x/(c-x):
p1:=plots:-implicitplot(eval(w,c=2),x=-6..9,y=-3..3):
p2:=plots:-implicitplot(eval(w,c=2),x=-6..10,y=-3..3):
p3:=plots:-implicitplot(eval(w,c=2),x=-6..11,y=-3..3):
[p1,p2,p3]

Gives

Notice p2. The vertical line is gone. This happens when the range x=-6..10 and it shows back again when x=-6..11 or x=-6..9

Why does this happen? It is the same equation.

I tried different things but can't figure how to make Maple give a simplified result from int command without these RootOf with sums in them. Here is an example.

restart;
anti:=int(1/(a+x^(1/5)),x);

The strange thing is that doing

eval(anti,a=1)

Keeps these rootsOf and Sums there. But doing

anti:=int(1/(1+x^(1/5)),x);

Gives simplified result without RootOf

I tried DEtools:-remove_RootOf and assumptions and value() but nothing worked. I tried assumptions on a, such as assuming a::integer,a>0 and other things. 

I need similar result as Mathematica:

ClearAll[x, a];
Integrate[1/(a + x^(1/5)), x]

I am sure there is an option in Maple to do that, i.e. give result without these RootOf and Sums. But so far, I could not find it. I looked at options to int() command also. 

Any one know what option to use or how to simplifies it the the above result by Mathematica? 

Maple 2022.1 on windows 10