  We report the first realization of a quantum degenerate mixture of bosonic
$^{87}$Rb and fermionic $^{171}$Yb atoms in a hybrid optical dipole trap with a
tunable, species-dependent trapping potential. $^{87}$Rb is shown to be a
viable refrigerant for the non-interacting $^{171}$Yb atoms, cooling up to $2.4
\times 10^5$ $^{171}$Yb atoms to a temperature of $T/T_F = 0.16(2) $ while
simultaneously forming a $^{87}$Rb BEC of $3.5 \times 10^5$ atoms. Furthermore
we demonstrate our ability to independently tailor the potentials for each
species, which paves the way for studying impurities immersed in a Bose gas.
