This paper reports results from a search for ν_μ → ν_e transitions by the MINOS experiment based on a 7×10^(20) protons-on-target exposure. Our observation of 54 candidate ν_e events in the far detector with a background of 49.1±7.0(stat)±2.7(syst) events predicted by the measurements in the near detector requires 2sin^2(2θ_(13))sin^2θ_(23)<0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at δ_(CP)=0. The experiment sets the tightest limits to date on the value of θ_(13) for nearly all values of δ_(CP) for the normal neutrino mass hierarchy and maximal sin^2(2θ_(23))
