Mathamatics And riddels

There exist the integral from a to a of f(x) entities who are your friends.

Topologists fail to discern the difference between a doughnut and a coffee cup.

The integral of (1/cabin) is a houseboat.

I've got one that ties in with the movement of the chess knight.

Suppose I have a calculator which displays ten digits. How many distinct ten digit numbers can I type into my calculator using 0-9 keys once each, and moving from one keypress to another using the knight's move in chess?

Here's an extraordinarily enjoyable task: Write an equation that uses pi exactly four times and equals n such that n is a positive or negative integer. You can use the common functions such as sine, cosine, logarithm, etc. (Understandably, you may already know the solution to this problem).