  The Hubble Space Telescope (HST) and the Kepler space mission observed a
large number of planetary transits showing anomalies due to starspot eclipses,
with more such observations expected in the near future by the K2 mission and
the Transiting Exoplanet Survey Satellite (TESS). To facilitate analysis of
this phenomenon, we present spotrod, a model for planetary transits of stars
with an arbitrary limb darkening law and a number of homogeneous, circular
spots on their surface. A free, open source implementation written in C, ready
to use in Python, is available for download.
  We analyze Kepler observations of the planetary host star HAT-P-11, and study
the size and contrast of more than two hundred starspots. We find that the flux
ratio of spots ranges at least from 0.6 to 0.9, corresponding to an effective
temperature approximately 100 to 450 K lower than the stellar surface, although
it is possible that some spots are darker than 0.5. The largest detected spots
have a radius less than approximately 0.2 stellar radii.
