Your worksheet doesn't have theta, so I'm guessing you want f'(1). The output of dsolve can be used to get this, e.g., c1(1) gives

[x = 1., f(x) = 1.00000000000000, diff(f(x), x) = 0.294118092731875] 

and so to extract the value 0.294118092731875 use eval(diff(f(x), x), c1(1)).

@Carl Love I added a 60 Digit calculation to the 30 digit one

evalf[30](eval([p, sinnx, p - sinnx], x = -1.95));
evalf[60](eval([p, sinnx, p - sinnx], x = -1.95));

 (errors (p-sinnx) ca. 10^(-13) for 30 digits and 10^(-43) for 60 digits.)

At 30 digits I was thinking there was a true error because Maple usually does much better than half the digits correct. But since the functions are identical, I increased to 60, which shows how poor the 30 Digit one was.

@Carl Love Thanks for the resolution of the identical/approx issue. Nice solution for the plot - vote up.

@FDS I get the same as you on Maple 2024.1 on Windows. Opening the Excel file in Excel (Office 365) everything looks fine. So that is a mystery; perhaps contact technical support. 

@vv On my Maple 2024.1, I get the same as you got on Maple 2018.

@FDS So why not upload a small excel file that doesn't work for you, to see if we get the same results, or can figure out if there is something about your file that might make a difference.

@felixiao You mean you want to find that there are three peaks? This is a nontrivial task - you need to numerically differentiate the data and then find where it crosses zero. It is easiest to do this visually - use the plot probe to see the max values and where they occur. I just split the data into ranges and did the max on each. You can use max[index] to find which N value the maximum occurs at.

MMSE_2re.mw

@felixiao Please upload the worksheet finding the maximum of KR[N].

I don't know an automatic way to get the indenting. I usually do this manually within the startup code window, with a bunch of "enter", "tab" and "delete". As a bonus, the diagnostics pane at the bottom tells you about unused variables etc (no errors in this case though).

For killing command completion, look at the choices under tools -> options -> interface.

@emendes try

procnames:=select(type,[anames('user')],procedure)[];
save procnames, cat(currentdir(),"/myprocs.mpl");

@FDS I think @Thomas Richard is asking you what happens if you use his method on your Excel file.

Here it is. Note that i+(j-1)*N was only used for the ordering of of the c[i,j](t) variables to save having the large list Vars in memory and passed to makeproc; the indexing of j11 was as in your original code and was not using i+(j-1)*N. But this is safer in the sense that if you change the ordering in Vars, the code will still work.

makeproctestnew2.mw

Although my codes are more stable in the sense I can get them working to higher N, they still lose connection to the kernel for some combinations of the task size and N, even though they do not output to the global arrays j11 and Equation, so it seems @Carl Love's conjecture is not correct, or is only part of the story. 

@C_R OK, I see you know it is in procedurelist form. I think the simplest is going to be sln(0) and look at the output. At least for an initial value problem you can enter any value, e.g., sln(-75), so long as it doesn't hit a singularity. It seems the sort of thing that infolevel[dsolve] might output, but no luck there.

Edit: If output = listprocedure, you see the variables in the output of dsolve, but perhaps changing the dsolve command is not allowed.

I have a vague recollection of having this issue, and the solution was to run the update from an administrator account (not just running as administrator from a non-administrator account).

@MaPal93 Looks OK. You need local gamma;