We have measured, as a function of transverse momentum (p⊥), the invariant cross section Edσd3p for the production of π+/-, K+/-, p, p̄, d, and d̄ in proton collisions with a tungsten (W) target at incident proton energies of 200, 300, and 400 GeV. The measurements were made in the region of 90° in the c.m. system of the incident proton and a single nucleon at rest. Measurements were also made with 300-GeV protons incident on Be, Ti, and W targets of equal interaction length. These p-nucleus measurements, which show a strong dependence on atomic number at high p⊥, were used to extract effective proton-nucleon cross sections by extrapolation to atomic number unity. At large values of the scaling variable x⊥=2p⊥s, where s is the square of the c.m. energy, the pion data are found to be well represented by the expression (s)-ne-ax⊥, with n=11.0+/-0.4 and a=36.0+/-0.4. x⊥<0.35, where similar measurements have been made at the CERN ISR, our data are in good agreement with the ISR data.