I think the fact that the former Maple UI was better and faster can be proved mathematically :-)

@Alfred_F  To factor, just use:

evalindets(%, `^`, factor);

                      81*(x-5)^4 + 117649*(y-11)^6 + 256*(z-13)^8

@C_R 

    The term residual for an antiderivative does not make sense.
    The constant depends on the method of integration, even in the simplest cases.
    For example:
 ∫(x+1)dx = 1/2(x+1)²   if we use the formula ∫(ax+b)ⁿdx=(1/a)(((ax+b)ⁿ⁺¹)/(n+1))
    but
∫(x+1)dx = 1/2x²+x   if we integrate term by term.

@C_R 

int(D(tanh)(x), x);
diff(%, x);
simplify(%) = D(tanh)(x);  ###
is(%);

@nm  For implicitplot,  rhs(sol) is not needed.

@dharr  This problem is known and treated in Odrzywolek' paper. It can be also solved by changing the argument function from (-Pi,Pi] to [-Pi,Pi). Anyway, it's a game ...

A good idea for Maplesoft would be to enhance the Maple Kernel for Jupyter. It works ok, but some useful elements of the GUI (e.g. the animations) are still missing.

I cannot understand why the user was forced to use a worse GUI.

@Rouben Rostamian   The evaluation is obvious after the change of variables r^4 = u. Maple computes the limit at once but by hand too..

[moderator:

Download RRint.mw]

Unfortunately, this problem reveals (again and again!) two of Maple's shortcomings:

1. The dificulty to obtain higher precision: just try e.g. Digits:=25.
2. The imposibility to interrupt the computations using the bottom button.

For the record: i have corrected the input f:=  (noticed by  sand15) and i have added the identify command

Actually, in Maple it is possible to define the vertices of the polygon simply by clicking! You have to use the so called Embedded components.

For an example, just type ?examples,ProgrammaticContentGeneration and execute the commands in this worksheet to see how it works (press Enter several times and click a few times in the plot when it appears). See my answer below for a minimal version.

@acer  As I remember, years ago, sometimes, it could be necessary to install some version of 
Visual C++ Redistributable for Visual Studio.

@Alfred_F  I use 1d input and 2d output. Maple promotes now 2d input; it looks nicer but may introduce hidden characters hard to detect, so, non-working code. 2d input has some limitations too; note that the 2d notation is internally converted to 1d. I prefer the old school.

@Alfred_F You are using 2d input; just replace the last line with:

lprint(cat("That's all for x <=y <= z <= ", N))

are quickly found by Maple:

restart;
s1:=x+y+z: s2:=x*y+x*z+y*z: s3:=x*y*z:
N:=1000:
for x to N do for y from x to N do for z from y to N do
  if isqrt(s1)^2=s1 and isqrt(s2)^2=s2 and isqrt(s3)^2=s3
     then lprint([x,y,z]) fi;
od od od:
lprint("That's all for x <=y <= z <= " || N);

[45, 64, 180]
[65, 104, 360]
[72, 136, 153]
[80, 225, 320]
[98, 272, 306]
[180, 256, 720]
[272, 306, 578]
[288, 544, 612]
That's all for x <=y <= z <= 1000