I'm looking for a solution to the following integral.

$$\int_{\lambda}^{y}(x-a)^{-b}x^{-c}\exp\left( -d x^{-e} \right)dx,$$ where $a > 0$, $a < \lambda$, $\lambda>0$, $b > 0$, $c > 0$, $d > 0$, $e > 0$, and $y > \lambda$.

This equation appears in the context of Physical Layer Security, which is an area of study in digital communications (telecom).