In computer science, most languages incorporate integer division and integer multiplication (even if the initial values are decimals, the result will always be an integer - probably by truncating or rounding the decimal part), and they have simple mathematical definitions. Is there such an operation for taking the "integer power" of a number?
For instance, lets say I want to do $10^{1.5}$, the answer would be $32$ instead of $31.6228$. Likewise, if I did $1.5^{10}$, the answer would be $58$ instead of $57.665$. Is there a formula for such an operation?
You can use the floor and ceiling functions to accomplish this -- or for any other operation, really.
If you want to truncate the decimal, you'd use the floor function:
$$\lfloor 10^{1.5} \rfloor = 57.$$
If you want to round up, you'd use the ceiling function:
$$\lceil 10^{1.5} \rceil = 58.$$
If you want to round to the nearer integer, you can check the decimal part like this:
$$10^{1.5}-\lfloor 10^{1.5}\rfloor \doteq 0.665,$$
and then use the appropriate function.