  We present radio and X-ray observations of the nearby Type IIb Supernova
2013df in NGC4414 from 10 to 250 days after the explosion. The radio emission
showed a peculiar soft-to-hard spectral evolution. We present a model in which
inverse Compton cooling of synchrotron emitting electrons can account for the
observed spectral and light curve evolution. A significant mass loss rate,
$\dot{M} \approx 8 \times 10^{-5}\,\rm M_{\odot}/yr$ for a wind velocity of 10
km/s, is estimated from the detailed modeling of radio and X-ray emission,
which are primarily due to synchrotron and bremsstrahlung, respectively. We
show that SN 2013df is similar to SN 1993J in various ways. The shock wave
speed of SN 2013df was found to be average among the radio supernovae;
$v_{sh}/c \sim 0.07$. We did not find any significant deviation from smooth
decline in the light curve of SN 2013df. One of the main results of our
self-consistent multiband modeling is the significant deviation from energy
equipartition between magnetic fields and relativistic electrons behind the
shock. We estimate $\epsilon_{e} = 200 \epsilon_{B}$. In general for Type IIb
SNe, we find that the presence of bright optical cooling envelope emission is
linked with free-free radio absorption and bright thermal X-ray emission. This
finding suggests that more extended progenitors, similar to that of SN 2013df,
suffer from substantial mass loss in the years before the supernova.
