@Adam Ledger And the final results shown are different, in your last uploaded Document. Some instances involving "VAGRANTASP\\Adam" in the previous Document's output are no longer there.

But we cannot tell for sure what different effect has been made, because you still haven't bothered to upload a data file that contains a representative example that reproduces the problem.

@Carl Love Use of those mixes of options to solve -- as well as a further real option, which also sometimes has effects that are not documented -- is one of the things that Calculus1:-Roots tries internally (using environment variables to control those options).

But Calculus1:-Roots also does more, including some checks that solutions are valid. In the recent past some version's solve would sometimes emit too many results, some of which weren't actual solutions. The trig case was one of the offenders. It still happens now and then when using solve and trig equations, though less often.

In addition, the call to solve which you've given does not work for this particular example in Maple 2018 and earlier. But this example works using Calculus1:-Roots at least as far back as Maple 11.

This is why I consider Calculus1:-Roots to be still the best choice for this particular class of problem (univariate, trig involved, real root required, and not too complicated). I have examples where it still does better than solve, even with the user trying all the special options combinations. I have less examples of the opposite. (I've looked at many examples.)

I agree that RealDomain:-solve is often not the best choice. It tries to "solve over the reals", in a sometimes stricter sense than merely restricting final results to the reals. That's not so tenable or practical in Maple.

@Adam Ledger I am not sure that you understood my point. It seems to me that your output shows that the string in the imported data is actually "VAGRANTASP\\Adam" . It ought to be easy enough to make a few checks to see whether that is the case.

You could simply lprint the imported data (before any processing) and look.

And if it is the case, then your predicate ought to use that same string in its test. It looks like it is not doing so. It looks to me as if your original predicate is using a string that doesn't actually contain a backslash character.

I could be mistaken, as you've only shown awkward 2D Input (which is not helpful here, as it adds another layer of possible error). And you haven't bothered to upload the actual data, so we only get to see the pretty-printed output.

@Zeineb I already knew some ways to demonstrate that it's true, thanks. I was simply suggesting that you could consider it, if you were wary that I'd taken off the sqrt on this example.

It wasn't clear whether you wanted a programmatic means.

@zjervoj97 So, why didn't you supply those ranges as arguments to fsolve?

My Answer's last example already showed how you could supply a complex box as domain, and supplying real ranges is done similarly and even more easily. All you had to do was type in the ranges that you knew.

You didn't mention the restriction when you originally asked the question here.

Your question is broad and vague. It would help if your query was as specific as possible for your goal.

Are you thinking of examples that might involve generating functions (possibly accessible via gfun, rsolve, dsolve, etc)?

Put you followup queries on this example here, as Reply to the original Question.

Duplicate question threads on this will be flagged as such, and may be deleted.

@Thomas Dean Thank you, and sorry if I was harsh.

We all sometimes have difficulty imagining the mindset of others. I know I do. That is as true of us here as it is of the authors of the manuals.

@Thomas Dean  It's disappointing when people ask questions here and provide only the vaguest reference and snippet with even a proper example that shows what they're asking.

It would have been polite and useful if you'd simply provided your example up front.

What work have you done so far with this homework question? Where did you get stuck?

Put all your Fibonacci homework questions here. Don't post them in multiple threads, where they'll get flagged as duplicates for deletion.

Show what work you've done so far; this is not a homework-service.

Put your revised integral here, either in the Question body as attachment or in a Reply/Comment.

A duplicate Question thread is unhelpful and unnecessary and will be flagged as a duplicate (which may be deleted).

@emendes Please explain why your solution excluding both alpha[2,3] and alpha[3,5] is optimal or best. Earlier, you wrote, "reduce as much as possible". What if you could exclude just a single variable, would that be better still?

Are you trying to find a minimal set of equations, or unconflicted variables? How do you break ties?

Provide a rigorous definition of what you want.

Please explain all these points clearly, and not just a partial or incomplete answer to one of them. (It's not really enough to see you agree with someone else's suggestion. At this point you really need to state precisely what it is that you want.)

@Carl Love Taking his followup example, with the equations in a list eqns in the order written, I don't see whether he might be asking for, say,

   eqns[1,2,3,4,5,6,7,8,9,10]
or,
   eqns[1,2,3,4,6,7,8,9,10,11]
or,
   eqns[1,2,3,4,6,7,8,9,10]

And, for general examples, I don't really see how he is specifying any choice that can arise (in equations or variables to omit).
   

You appear to be using square brackets as some kind of expression delimiter for grouping terms arithmetically, which is incorrect. You need to use round brackets for that. Square brackets denote lists.