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Using the CLEO III detector, we measure absolute cross sections for e+e- ->hadrons at seven center-of-mass energies between 6.964 and 10.538 GeV. R, theratio of hadronic and muon pair production cross sections, is measured at theseenergies with a r.m.s. error <2% allowing determinations of the strong couplingalpha_s. Using the expected evolution of alpha_s with energy we findalpha_s(M_Z^2)=0.126 +/- 0.005 ^{+0.015}_{-0.011}, andLambda=0.31^{+0.09+0.29}_{-0.08-0.21}.

Measurement of sigma_Total in e+e- Annihilations Below 10.56 GeV