We study the equilibrium folding/unfolding thermodynamics of a small globular miniprotein, the Tip cage, that is confined to the interior of a 2 nm radius fullerene ball. The interactions of the fullerene surface are changed from nonpolar to polar to mimic the interior of the GroEL/ES chaperonin that assists proteins to fold in vivo. We find that nonpolar confinement stabilizes the folded state of the protein due to the effects of volume reduction that destabilize the unfolded state and also due to interactions with the fullerene surface. For the Tip cage, polar confinement has a net destabilizing effect that results from the stabilizing confinement and the competitive exclusion effect that keeps the protein away from the surface hydration shell and stronger interactions between charged side chains in the protein and the polar surface that compete against the formation of an ion pair that stabilizes the protein folded state. We show that confinement effects due to volume reduction can be overcome by sequence-specific interactions of the protein side chains with the encapsulating surface. This study shows that there is a complex balance among many competing effects that determine the mechanism of GroEL chaperonin in enhancing the folding rate of polypeptide inside its cavity.