@sursumCorda 
Formaly I would say yes.
However, I did not think that far to use an argument inside a function composition.
This challenges my imagingation. The only Maple function I know that could fit for g into your example that uses two pairs of parentheses is D. 
What else could make sense?

@sursumCorda 

The desired output is inside the first pair of parentheses of the rhs of the below equations. The argument of the function applications is in the second pair of parentheses

f(g(h(x), x))=(f@g)(h(x),x);
f(g(x)(h(x)))=(f)(g(x)*h(x));# not a function composition
f(g(D(x)))=(f@d@D)(x);
f(g(h(x)()))=(f@g@h(x))()

I assume you know the connetion of the above to apply

op(0..1,'(f@g)(h(x),x)');
apply(%)

@Carl Love 

I tried entering tags in the message editor in the past but observed after saving a draft that newly entered tags were not listed. So tags are only added after sending.

I will give it another try.

Thank you

@sand15

I have tried "Deep Research" (GTP 5.6 EU) to get the anual profiles of questions asked per month to better identify AI effects.

This did not work. AI took a long time to give a negative answer and proposed what I could do instead. Apparently, HTML tags that identify the publication date, which are retrievable for a human through a web browser, were not retrievable by the deep researcher.

Apart from that I share the frustration caused by the negative impact of AI on user communities in general and in particular on MaplePrimes.

We risk losing the beauty of elegant Maple coding from humans for humans and replacing it with flat and voluminous Phyton/C implementations translated directly to Maple. The next generation of Maple users will not learn from AI how to exploit the strength of Maple. Maple risks becoming an ordinary and replaceable product.

At least, MapleAI could apart from the disclaimer that answers could be wrong also mention MaplePrimes as a resource from time to time.

You normally need a license code to install Maple 2024 and a Maplesoft Product Download Link. See here for details:
https://www.maplesoft.com/support/downloads/index.aspx

If you have a valid license Maplesoft might give you access to older versions but for this you have to contact them, because each version of Maple comes with a separate license code.

@Ronan 
Strange. I cannot do this. When I right click on running instances of Maple in the task bar, I only get the option to close the window. Other applications can be pinned. Maybe I can't do this because the applications are pinned to the start menu.

I any case, I do not see why pinning to the task bar should make a difference to pinning to the start menu (which allows chaning the kernel mode on my installation)

@Ronan 

You could try it manually by setting  in the ini file
C:\Users\<your-user-name>\AppData\Roaming\Maple\<version>\Maple.ini

If you can't find the ini file there it is stored where Maple is installed and it is only changeable if you start Maple as Admin.

@Jean-Michel 

Strange. I would give it a second try. Uninstall everything, restart your computer, log-in as admin (automatic updating Maple on my machine with a user account does not work), install the 2026.0 distribution (installing the update 2026.1 without a preexisting Maple version will not work), test this distribution and then update to 2026.1.

I once had a corrupted download file. Only with a new download I could propperly install Maple. These cases are rare but you might want to try a fresh download as well.

If it does not work, you have to contact support.

To reproduce or compare it to own observations, more details are needed.
Does the GUI not work at all or do you experience unresposiveness after loading or executing and worksheet?

@vv 

You are rigth. I changed to antiderivative difference. Thank you

@acer 
The additive constant fit's to ?Definition,antiderivative and ?Definition,integrate in Maple's help system.
So, the results seems to be formally correct (consistent within Maple), but most likely not desired, because the area under the function
D(tanh)(z)

cannot be computed (at least plotted) when z is real valued. This is because the magnitude of "residual" antiderivative difference is zero in the complex plane (note also the arument jumps )

ad_difference := int(D(tanh)(z), z) - tanh(z);
sc := 4;
plots:-complexplot3d(Re(`%%`), z = -sc - sc*I .. sc + sc*I);

but leads to numerical exceptions when evaluated on the real line.

If have tried to understand whether whatever Maple adds to tanh could be related to an identity. The closest I get is of same magnitude but opposite argument

0 = tanh(z) - int(D(tanh)(z), z);
2*(% + z);
map(exp, %);
simplify(%);
convert(%, exp);
simplify(%);

There are plenty of examples here in this forum which are in line with what you said. However it's not easy to find the pearls. 
For a particular problem I suggest asking for examples and/or posting an exemplary version of a problem.

You might not have discovered ?codegen,optimize. Another way to speed-up computation. There is also the package ?CUDA which is supposed to accellerate certain linear algebra routines (it might not work on your local setting).

And if you have the time and are interested in the Maple language and effcient coding, read the ProgrammingGuide. 
 

@vv 
Thank you for correcting me. Since an identity is returned and the below does not show any singularities on the real line

sc := 2;
int(D(tanh)(z), z);
subs(z = re + im*I, %);
plot3d(Re(%), re = -sc .. sc, im = -sc .. sc, title = 'Re');
plot3d(Im(`%%`), re = -sc .. sc, im = -sc .. sc, title = 'Im');

one could assume that result is correct.
However, I could not find a way to combine the logarithmic terms in a way that the result equals tanh. The result does not seem to be valid for the real line

int(D(tanh)(z), z);
combine(%, ln) assuming real;
op([1, 1], %);
plot(%/I, title = %/I);

If I am not again mistaken, the methods returning the result with ln terms should have been listed under FAILS as listed here

int(D(tanh)(z), z, method = _RETURNVERBOSE)

Maybe there is a proof that the result from my original post minus tanh(x) is zero. I do not see this here

sc := 10;
int(D(tanh)(z), z) - tanh(z);
subs(z = re + im*I, %);
plot3d(Re(%), re = -sc .. sc, im = -sc .. sc, title = 'Re');
plot3d(Im(`%%`), re = -sc .. sc, im = -sc .. sc, title = 'Im');

This looks wrong to me on the whole complex plane

@Gillee 

Only for the records, in case someone else want's to make CUDA work:

Today I reset my NVIDA to factory settings. How I get this

Under https://developer.nvidia.com/cuda/gpus I found out that my card is not listed. However your card is listed (i.e. should be supported)...

I also saw that now under Windows 11, the use of the NVIDIA card cannot be configured anymore with the NVIDIA tool. The configuration is managed fully by Windows 11. I tried (before resetting the card) to enable and disable a few settings but did not notice a huge change in performance.

@acer 
Since tanh is elementary I did not consider to use methods but I tried assuming real. I also tried some convert options.

With my limited math background I could not conclude whether the returned result of the default method is correct (under certain restrictions). I would say no in case the below is sufficient proof

int(D(tanh)(x), x);
diff(%, x);
simplify(%) = tanh(x);
is(%);
                    1                   1                
      x + tanh(x) + - ln(tanh(x) - 1) - - ln(tanh(x) + 1)
                    2                   2                

                              2          
                       sech(x)  = tanh(x)

                             false