Off-lattice Monte Carlo simulations on semiflexible polymer chains with and without excluded volume interactions have been performed. The model used in the simulations is a discrete representation of the worm-like chain model of Kratky and Pored applied in the pseudocontinuous limit. The ratio between the cross-section radius R of the chain and the statistical segment length b was chosen to be R/b = 0.1 which corresponds to the value found for polymer-like micelles. The ratio R/b is equivalent to a reduced binary cluster integral of B = 0.30, which is in accordance with the value for polystyrene in a good solvent. The scattering functions of the semiflexible chains have been determined with a precision of 1-2% for L/b = 0.3-640, where L is the contour length of the chain. Numerical approximations to these functions have been determined which interpolate between the simulated functions, and these can be used in the analysis of experimental scattering data. The approximations have been used in least-squares fitting of experimental small-angle neutron scattering data from polystyrene in a good solvent.