Quiz: calculating a definite integral

[Thomas Klemm]

Let's assume we want to calculate the following definite integral:
\[ \int_{0}^{1}x^{-x}dx \]
We'd use a calculator with an \( \int_{x}^{y} \) button and write a short program:

01 LBL 0
02 CHS
03 \(y^x\)
04 RTN

The result is something like: 1.291285997
Now what if for some reason this button doesn't work or we don't have a calculator that supports numerical integration?
How can we still calculate this definite integral?

Cheers
Thomas

Addendum:
How can I guide you into the right direction without spoiling the quiz?
Of course you can just use another calculator where the button isn't broken.
But that's not the point of this quiz.