$MCE_{Q}$ - numerical code for inclusive lepton flux calculations

Calculations of atmospheric lepton spectra at very high energy experience a revived interest after the detection of the diffuse astrophysical neutrino flux by the IceCube observatory. In order to determine its spectral index and normalization with higher accuracy, the uncertainties of the atmospheric background have to modelled correctly and taken into account in the experimental fits. The available schemes, like a semi-analytic approach or Monte Carlo methods suffer either from a lack of detail or use too much CPU time and become inefficient. We have developed a numerical code based for the full system of coupled cascade equations which is shaped towards an efficient calculation of fluxes and achieves very high precision, comparable with Monte Carlo methods. Special attention lies on predictions of the prompt lepton flux using interchangeable physical parametrizations. Other features include detailed insight into hadrons participating in the cascade, the atmospheric density profiles and no restrictions on the definition of the primary cosmic ray flux.