  We give a method of sub-exponential complexity to approximate the volume of
the intersection of the unit hypercube with two specific sets. Our method can
be applied (without losing the sub-exponential complexity) to compute the
volume of the hypercube intersected with a fixed number of sets, described by
the equations of the form $\sum_{q=1}^n a_q(x_q) = b$, where $a_q : \mathbb{R}
\to \mathbb{R}$ are polynomial functions and $b \in \mathbb{R}$. Note that the
resulting sets are not necessarily convex. However, this type of equations
describe, among others, half-spaces, balls and ellipsoids.
