[seanhunter]

It depends on the subject. Here in the UK calculators are absolutely expected in most STEM exams for high school and university.

For a trig exam for example if you don't allow calculators you are very limited in terms of what you can do. You could do a lot of trig identities etc but all the problems with a concrete answer would have to boil down to some sort of 30/60/90 or 45/45/90 right triangle. It's not reasonable to expect people to be able to calculate exponents and logarithms in their heads either beyond very simple integer bases and small powers. Forget about natural logs for instance. Likewise anything which depends on trig, exponents, logs etc eg converting rectangular complex coordinates to polar, adding vectors fitting any kind of exponential model, etc.

For a stats exam calculating things like standard deviation etc are almost unbearably tedious with a calculator let alone without, but you do need to be able to demonstrate you can do it.