  Self-force theory is the leading method of modeling extreme-mass-ratio
inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is
well known that for an accurate EMRI model, second-order self-force effects are
critical, but calculations of these effects have been beset by obstacles. In
this letter we present the first implementation of a complete scheme for
second-order self-force computations, specialized to the case of quasicircular
orbits about a Schwarzschild black hole. As a demonstration, we calculate the
gravitational binding energy of these binaries.
