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 en
ergies of $7$ and $8mathrm{,TeV}$. 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^+rightarrowphi 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 $B^+rightarrow K^+pi^+pi^-mu^{+}mu^{-}$.
Evidence for the hadronic annihilation decay mode $B^{+} to D_s^{+}phi$ is found with greater than $3sigma$ significance. The branching fraction and CP asymmetry are measured to be mathcal{B}(B^{+} to D_s^{+}phi) &=& (1.87^{+1.25}_{-0.73}({rm stat})
pm 0.19 ({rm syst}) pm 0.32 ({rm norm})) times 10^{-6}, mathcal{A}_{CP}(B^{+} to D_s^{+}phi) &=& -0.01 pm 0.41 ({rm stat}) pm 0.03 ({rm syst}). The last uncertainty on $mathcal{B}(B^{+} to D_s^{+}phi)$ is from the branching fractions of the $B^+ to D_s^+ kern 0.2embar{kern -0.2em D}{}^0$ normalization mode and intermediate resonance decays. Upper limits are also set for the branching fractions of the related decay modes $B^{+}_{(c)} to D^{+}_{(s)} K^{*0}$, $B^{+}_{(c)} to D^{+}_{(s)} kern 0.2embar{kern -0.2em K}{}^{*0}$ and ${B_c^{+} to D^{+}_{s}phi}$, including the result ${mathcal{B}(B^+ to D^+ K^{*0})} < 1.8 times 10^{-6}$ at the 90% credibility level.
