  First observations of the rare decays $B^+\rightarrow
K^+\pi^+\pi^-\mu^+\mu^-$ and $B^+\rightarrow \phi K^+\mu^+\mu^-$ are presented
using data corresponding to an integrated luminosity of $3.0\,{fb}^{-1}$,
collected by the LHCb experiment at centre-of-mass energies of $7$ and
$8\mathrm{\,TeV}$. The branching fractions of the decays are \begin{eqnarray*}
\mathcal{B}(B^+\rightarrow K^+\pi^+\pi^-\mu^+\mu^-) &=&
(4.36\,^{+0.29}_{-0.27}\,\mathrm{(stat)}\pm
0.21\,\mathrm{(syst)}\pm0.18\,\mathrm{(norm)})\times10^{-7},\\
\mathcal{B}(B^+\rightarrow\phi K^+\mu^+\mu^-) &=& (0.82
\,^{+0.19}_{-0.17}\,\mathrm{(stat)}\,^{+0.10}_{-0.04}\,\mathrm{(syst)}\pm0.27\,\mathrm{(norm)})
\times10^{-7},\end{eqnarray*} where the uncertainties are statistical,
systematic, and due to the uncertainty on the branching fractions of the
normalisation modes. A measurement of the differential branching fraction in
bins of the invariant mass squared of the dimuon system is also presented for
the decay $B^+\rightarrow K^+\pi^+\pi^-\mu^{+}\mu^{-}$.
