The cross-section for inelastic proton-proton collisions, with at least one prompt long-lived charged particle of transverse momentum P-T > 0.2GeV/c in the pseudorapidity range 2.0 < eta < 4.5, is measured by the 1:11Cb experiment at a centre-of-mass energy of root s = 7 TeV. The cross-section in this kinematic range is determined to be sigma(accc)(inel) = 55.0 +/- 2.4 nib with an experimental uncertainty that is dominated by systematic contributions. Extrapolation to the full phase space, using PYTHIA 6, yields sigma(inel) = 66.9 +/- 2.9 +/- 4.4 nib, where the first uncertainty is experimental and the second is due to the extrapolation.
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