@acer 

Very Impressive!! Thank you very much

@Christian Wolinski Thanks for the advice.

I used fsolve(SYS,VAR,fulldigits) in combination with Digits:=15:

With the standard 10 digits, the option fulldigits is not enough in this case.

This is the guidance I was looking for. Thanks a lot!

@tomleslie 

Thanks a lot for your answers.

It is indeed a bug. Amazing!

@nm 

Thanks for checking my question.
I added an Image of the problem in the main post.

Thanks again!

The issue is not the cycle, Now I realize, is that the contour generated _detours back_ to the first vertex instead of going to the third one.

My mistake. But anyway, feel free to explore the code. Any suggestions will be very much appreciated.

@nm 

Thanks a lot, this was so obvious I didn't even expected to work (for the infinity... would crash my PC)

Maple sometimes still amazes me, 20 years from my first time using it.

@tomleslie 

Hi, I'm very appreciated for your suggestion. Thanks a lot. However, it seems that I screwed too much Windows registry and no trick would suffice this time.

I had to create a new user account in my PC and move all my files there. Had I known better I would do that the first time, not needing to uninstall anything at all.

For future readers. Do not mess up with Windows registry if there is another way around.

Best regards
 

@Preben Alsholm 

My good sir, thanks a lot.

That's just what I needed.

@Carl Love

This works, thanks a lot.

Have a nice day!

@Axel Vogt 

Thanks for your help. I still don't know why the result is so different.

@Carl Love 

Thanks a lot for your help :)

@Markiyan Hirnyk

I was unfamiliar with this DirectSearch command. I will give it a try...

Thnaks 

@vv 

Thanks

I think this is a good idea. I thought about using more digits to compute but I was unsure since that can increase computation time but I can set a conditional to increase digits only if no solutions are found.

Also I noticed that I can use solve with a maxsols oiptions to prevent multiple solutions. I don't know how Maple reach solutions in that case but it could work.

@Mac Dude 

Thanks a lot.

I'll try all those ideas.

@Carl Love @dharr 

Amazing. That's a very usefull command. For sure this will help me a lot.

(I wonder how come I had never seen it or need it before)

THANKS a lot, guys. Have you all a nice day.