Let $|q|<1$ and define the $q$-shifted factorials as $$(a;q)_{n} := \prod_{i=0}^{n-1} \left(1-a q^{i} \right) ,$$ with the limiting cases $$\left(a;q \right)_{0} = 1 $$ and $$\left( a;q \right)_{\infty} = \prod_{i=0}^{\infty} \left(1-a q^{i} \right) .$$
In the following article by M. E. Bachraoui, the following identities are stated in equations $(12)$ and $(13)$ for $|q|<1$ :
$$ \int_{- \frac{1}{2} \ln(q) }^{ \frac{1}{2} \ln(q) } \ln \left( q e^{\pm 2x} ; q^{2} \right)_{\infty} dx = \frac{\zeta(2)}{2}. $$
When I saw these identities, it was the first time I encountered a definite integral of a $q$-series or $q$-Pochhammer symbol. I haven't seen any since.
Question: what other definite integrals involving $q$-series have been evaluated in the past? Pointers to relevant references from the literature are much appreciated.