  In many cases one may encounter an integral which is of $q$-Mellin--Barnes
type. These integrals are easily evaluated using theorems which have a long
history dating back to Slater, Askey, Gasper, Rahman and others. We derive some
interesting $q$-Mellin--Barnes integrals and using them we derive
transformation and summation formulas for nonterminating basic hypergeometric
functions. The cases which we treat include ratios of theta functions, the
Askey--Wilson moments, nonterminating well-poised ${}_3\phi_2$, nonterminating
very-well-poised ${}_5W_4$, ${}_8W_7$, products of two nonterminating
${}_2\phi_1$'s, square of a nonterminating well-poised ${}_2\phi_1$, and
nonterminating ${}_{12}W_{11}$ and ${}_{10}W_9$.
