Integral of sec^2(x)
Perhaps I am inputting incorrectly but this is what I get

Perhaps I am inputting incorrectly but this is what I get

Can't be sure as you don't attach your sheet, but it looks like you have an invisible implicit multiplication operator between "sec" and the parentheses. So your integrands are "sec^2*x" and "sec*x^2", where "sec" is treated as an unknown.
If you fix that it should work as expected:

You can't use the first notation. While its a quite common and useful shortcut its not perfectly correct to just square the function name and so Mathcad does not accept it. In fact you even should not be able to enter it that way. Its probably from your try to enter it anyway which resulted in separating the function name from the argument and created that implicit multiplication.
If you really need that kind of notation, you could define a custom function for the square of sec but its not that good looking.

LT
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