What is the expectation of $X^2$ where X has a truncated normal distribution?

Question

Suppose that $X\sim N\left(a,\mbox{ }\sigma^{2}\right)$, what is $E\left\{ \left[1\left\{ X>b\right\} \exp\left(X\right)\right]^{2}\right\}$?

$b$ is a constant.