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We present an algorithm for the rapid numerical integration of atime-periodic ODE with a small dissipation term that is $C^1$ in the velocity.Such an ODE arises as a model of spin-orbit coupling in a star/planet system,and the motivation for devising a fast algorithm for its solution comes fromthe desire to estimate probability of capture in various solutions, via MonteCarlo simulation: the integration times are very long, since we are interestedin phenomena occurring on times similar to the formation time of the planets.The proposed algorithm is based on the High-order Euler Method (HEM) which wasdescribed in~\cite{hem}, and it requires computer algebra to set up the codefor its implementation. The pay-off is an overall increase in speed by a factorof about $7.5$ compared to standard numerical methods. Means for acceleratingthe purely numerical computation are also discussed

Numerics for the spin orbit equation of Makarov with constant eccentricity