  We provide a systematic account of integrability of the spherical mechanics
associated with the near horizon extremal Myers-Perry black hole in arbitrary
dimension for the special case that all rotation parameters are equal. The
integrability is established both in the original coordinates and in
action-angle variables. It is demonstrated that the spherical mechanics
associated with the black hole in d=2n+1 is maximally superintegrable, while
its counterpart related to the black hole in d=2n lacks for only one integral
of motion to be maximally superintegrable.
