@acer Thank you very much for your illuminating answer. Yes, it is the professional version of what I needed. I have been able to make GlobalSearch work by unevaluating the functions one step further

GlobalSearch(''zero_function1(a, b)^2 + zero_function2(a, b)^2'', pointrange = [a = -20 .. 0.5, b = 0 .. 20])

But I could not make fsolve work. I did not imagine it was an accuracy problem.

Thank you very much again.

@acer Thank you very much. This is exactly what I needed. I have never used these commands and I could not get what I needed by using Help. I do appreciate your help. Thank you again.

@acer The reason I need this is to be able to generate Fortran outputs and to be able to introduce comment lines (=strings) in the Fortran fine generated with Maple.

By the way, you were right: my OS is Linux (Ubuntu)

@acer Thank you very much for your answer. It is what I needed. Let me ask you one more question. Your three ways work fine but all of them write the strings starting from the beginning of the file. Imagine the file has already some text, how can I make any of these way write the strings starting from the last line of the file and not from the first one (erasing everything was already in the file)? Thank you very much.

@acer Thank you for letting us know that the bug is already reported.

@Preben Alsholm Yes, it seems evalf is safe, even for large Digits. I agree using plot as a play model to evaluate the functions is not good. Although I think Maple should revise the command so that outputs like those are not produced. It is worrying, at least. Thank you for all your responses.

@dharr Our actual program is too complicated (it combines calculations with Maple and Matlab). Since there seems to be something strange in the output we started to analyze piece by piece. We thought that the evaluation routine  might be wrong in Maple 2023 when Digits is large, since the plot command must use somehow the evaluation routine to generate the plots, I guess. Apparently evalf does not show this problem. We will look somewhere else. 

@Preben Alsholm Thank you for your answer. Yes, for plots your approach seems to solve the problem. If you look at the actual data Maple is plotting (without adaptive=true), the values are negative. So it has evaluated the function incorrectly. That was my point. I used the plot command as a toy model. My problem is the way Maple evaluates numerically expressions when Digits is large. Because I seem to get non-sense in my data when Digits=40.

@tomleslie Thank you very much for your answer. Yes, using add will do the job. This was a toy model of my real computation. But I do not need a closed formula for the summation. So your proposal will work for me.

Your approach will do either. Now I have several choices to solve the problem. Thank you very much.

Thank you very much. If I decide to use alias (which seems to be risky), both your suggestions will do.

The reason I chose alias was I had to solve vector partial differenctial equations. What I showed was the easiest case where I had the same problem I was finding when working on the real system (more functions and more variables). Best regards.

Thank you very much for your answer. Now it is clear to me what alias was doing. Regards.