The modular quantum dilogarithm was suggested by Faddeev in 1994
(in the theory of special functions it was called the hyperbolic gamma
function). It is built with the help of the simplest modular
transformation from the group SL(2,Z) applied to the q-Pochhammer
symbol. Recently a generalization of this function was suggested,
which uses an arbitrary transformation from SL(2,Z). In the talk I will
describe this function and present a proof of the evaluation formula
for a general univariate hyperbolic beta-integral built with its help.