The differential branching fraction of the rare decay b0 + is measured as a function of q2, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb1, collected by the LHCb experiment. Evidence of signal is observed in the q2 region below the square of the J/ mass. Integrating over 15 < q2 < 20 GeV2/c4 the differential branching fraction is measured asdb0+/dq2=1.180.08+0.09±0.03±0.27×107GeV2/c41,$$ \mathrm{d}\mathrm{\mathcal{B}}\left({\varLambda}_b^0\to \varLambda {\mu}^{+}{\mu}^{-}\right)/d{q}^2=\left({1.18}_{-0.08}^{+0.09}\pm 0.03\pm 0.27\right)\times {10}^{-7}{\left({\mathrm{GeV}}^2/{c}^4\right)}^{-1}, $$where the uncertainties are statistical, systematic and due to the normalisation mode, b0 J/, respectively. In the q2 intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon (AFB) and hadron (AFBh) systems are measured for the first time. In the range 15 < q2 < 20 GeV2/c4 they are found to beAFB=0.05±0.09stat±0.03systandAFBh=0.29±0.07stat±0.03syst.$$ \begin{array}{l}{A}_{\mathrm{FB}}^{\ell }=-0.05\pm 0.09\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right)\;\mathrm{and}\hfill \\ {}{A}_{\mathrm{FB}}^h=-0.29\pm 0.07\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right).\hfill \end{array} $$
