> Are there philosophical problems that have definite answers

Great question.

Within philosophical and epistemological frameworks, I could ask questions such as, "Can there be a square circle?"

Well, no, these two concepts have conflicting properties. A mathematician might think this a solved problem, but philosophy underpins our concept of concepts. Many philosophers spend a great deal arguing what is is.

For Plato, geometrical entities like circles and squares have distinct, perfect Forms. Forms have fixed essences, so a thing cannot participate in contradictory Forms at once.

Aristotle's law of noncontradiction says the same attribute cannot at the same time belong and not belong to the same subject in the same respect.

Theophrastus developed hypothetical syllogisms and refined Aristotle’s logic by distinguishing logical impossibilities from physical impossibilities.

Kant calls it an analytic contradiction, false by virtue of the concepts involved.

A mathematician takes these things for granted when working with equalities, logic and axioms, but they stand on philosophical roots. Mathematics assumes the consistency of concepts, but the question of why some concepts are consistent while others are impossible is a philosophical one. It's not a coincidence that so many ancient Greek mathematicians were also philosophers.