I forgot to remove the WRAPPER keyword from the define_external calls in one of those attachments. Could you please remove it, or download the now-edited first attachment in this Answer?

But since Control & Info are not structs then the WRAPPER option is not needed, and may be removed. And wrapperless external-calling doesn't need to compile anything, so hopefully that fixes that worksheet for you.

Where did the attachment go?

It is poor etiquette to include only an image of your expression, so that others can only test by retyping the supposed expression.

Instead, please be polite and upload and attach your actual worksheet that contains the expression. You can use the green up-arrow in the Mapleprimes editor for that.

Ensure that all other parameters have numeric values. What is the numeric value of Ea? Of F? Of Rrt? Is "PI" a mispelling of "Pi"? etc.

Also, if you have candidate ranges for the solving-variables then now is a good time to share such information.

Please don't put followup queries for this example in separate Question threads. Instead, just add it here. Eg. what happens at (0,0)?

@ContrapuntoBrowniano You marked your Question as "Maple 2018", and that is not the same as Maple 18.

Maple 18 was released in the year 2014. The Maple version naming scheme changed in the year 2015, to have the version number match the release year.

I will submit a report.

Download problem_etian2_rep.mw

@Chorux Sorry, I left in reference to another list I'd made. That should now be corrected, above.

Also, the code snippet $nops(L) may get rejected by the 2D parser, so I changed it to $1..nops(L) which should work in both 1D and 2D input modes.

@Rouben Rostamian  I saw it on the Help page in Maple 2022.0 for Topic plots:-display.

     redraw : boolean; specifies whether to allow redrawing of static
     2-D plots by combining the original plot calls into a single call
     rather than just displaying them together

I happened to have previously observed a (rare, hopefully, and now reported) case in which that new (default of) redraw=true caused a slowdown. So I was lucky to have had a little head start here.

Mentally I lump it in with explicitly adding the old defaulf of adaptive=true option for plot, that can help avoid some new slowdowns due to the adaptive=geometric in Maple 2022.0. Hopefully these things will be ironed out in 2022.1.

@vv I believe that the OP also wants this effect:

And someone might have an easier means to attain that.

@Christian Wolinski It appeared in Maple 2019.

See updates/Maple2019/Language.

I believe that I am making some progress, although I have to overcome the hurdle of the Control and Info options (structs, say) in the UMFPACK solver. But if I get it right then it could be exciting.

@C_R Please don't spawn off a separate Question thread for this (highly related, if not essentially duplicate) query, even if you haven't yet received a response here that satisfies you.

It runs quickly for me in Maple 2020.1 and 2020.2 for Linux.

@tomleslie This does not correspond to the provided definition.

Why do you want to write your own root-finding implementation for this, instead of using fsolve?