We present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS, and AR-chain(+) which we show outperform other methods in the literature and allow for fast, precise, and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. We show that AR-Sym6 and AR-chain(+), with algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, are the fastest and most accurate algorithms to treat black hole dynamics with extreme mass ratios, extreme eccentricities, and very close encounters. AR-Radau, the first regularized Radau integrator with round off error control down to 64 bits floating point machine precision, has the ability to handle extremely eccentric orbits and close approaches in long-term integrations. AR-ABITS, a bit efficient arbitrary precision method, achieves any precision with the least CPU cost compared to other open source arbitrary precision few-body codes. With the implementation of deep numerical and code optimization, these new algorithms in SpaceHub prove superior to other popular high precision few-body codes in terms of performance, accuracy, and speed.