I don’t care about the answer. I care about the thought process that went into finding the answer. The answer is irrelevant.
And making people do them in person with no technology is unrealistic - not because it can't be done, but because at that point, it's not a reflection of how you'd use it outside of that classroom, and people are going to call it pointless, and IMO they'd be right.
There’s body of knowledge a person trained in a given area ought to know without use of computers or notes. There are things a person who calls themself “an engineer” or “a physicist” ought to know off the top of their head. A person going into mechanical engineering ought to have some familiarity with how to integrate without using a computer. Such is my belief.