All computable functions from the computable reals to the computable reals are continuous. If your calculator reports an answer for 0^0, either the calculator noticed that the second 0 is rational (easy to do if you just type in "0", so check what happens if you put in something like tan(80 degrees) - tan(70 degrees) - tan(60 degrees) - tan(50 degrees)), or its calculations are wrong in some way. Most likely the second.