  We give an explicit form of the symplectic groupoid that integrates the
semiclassical standard Podles sphere. We show that Sheu's groupoid, whose
convolution C*-algebra quantizes the sphere, appears as the groupoid of the
Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic
groupoid. By using a complex polarization we recover the convolution algebra on
the space of polarized sections. We stress the role of the modular class in the
definition of the scalar product in order to get the correct quantum space.
