What lies at the core of human brain's processing, is it a simple retrieval from memory or actual computation?

For example, let’s say I am solving a tough Calculus problem, as is my friend.
I have practised calculus problems for several months now. While my friend is new to it.
So, I solve it easily while my friend struggles.
The Problem is a mix of the ones that I have done, so I can’t recall the solution directly from memory.
Now, what exactly can we attribute my solution to?
Do my neurons mix and match stuff from various different memory locations to find an answer, or is my "Activation Function" so well developed, that I can "compute at will" quick and error-free?
If it’s the former, high IQ is literally attributed to a good memory and retrieval from the memory system.
Only if its the latter, can we attribute "better processing" to high IQ?
Thoughts?

PS:- Simple arithmetics Calculations & algebra can be "direct computation" but manipulating/applying known formulae and concepts, does that come under "memory" or "computation"?