We measure the absolute branching fractions of \Ds semileptonic decays where the hadron in the final state is one of ϕ, η, \etap, \Ks, \Kstar, and f0, using 2.8×105\epm→\Ds\Dsstar decays collected in the CLEO-c detector at a center-of-mass energy close to 4170 MeV. We obtain B(\Dsp→ϕe+νe)=(2.29±0.37±0.11)%, B(\Dsp→ηe+νe)=(2.48±0.29±0.13)%, B(\Dsp→\etape+νe)=(0.91±0.33±0.05)%, where the first uncertainties are statistical and the second are systematic. We also obtain B(\Dsp→K0e+νe)=(0.37±0.10±0.02)%, and B(\Dsp→K⋆0e+νe)=(0.18±0.07±0.01)%, which are the first measurements of Cabibbo suppressed exclusive \Ds semileptonic decays, and, B(\Dsp→f0e+νe)×B(f0→\pip\pim)=(0.13±0.04±0.01)%. This is the first direct evidence of a semileptonic decay including a scalar meson in the final state.