In this study, a recently proposed integral wall model and concurrent inflow generation technique are applied in Large-Eddy-Simulation (iWMLES) of developing turbulent boundary layer flow over cuboidal roughness. We examine the performance of this integral wall model at various Reynolds numbers. The integral wall model is based on the von-Karman-Pohlhausen integral method. With several parameters in the proposed functional form of the velocity profile determined from the local flow conditions, the wall model predicts velocity profiles that satisfy the vertically integrated momentum equation. Only an algebraic system must be solved in the wall model which thus preserves the essential economy of equilibrium type models. The rough wall inflow generation technique is proposed based on a new definition of a length scale that is appropriate for the roughness dominated inner layer. It extends the rescaling-recycling method to rough surfaces. The integral wall model and the rough wall rescaling-recycling method are applied in Large Eddy Simulations of turbulent boundary layers over surface with distributed cuboidal roughness. The effect of Reynolds number is studied. A good agreement is found between the roughness function (velocity shift) measured in iWMLES and the Colebrook formula and previous experimental measurements.