Weakly attractive interactions between the tips of rodlike colloidal particles affect their liquid-crystal phase behavior due to a subtle interplay between enthalpy and entropy. Here we employ molecular dynamics simulations on semiflexible, repulsive bead-spring chains where one of the two end beads attract each other. We calculate the phase diagram as a function of both the volume fraction of the chains and the strength of the attractive potential. We identify a large number of phases that include isotropic, nematic, smectic-A, smectic-B, and crystalline states. For tip attraction energies lower than the thermal energy, our results are qualitatively consistent with experimental findings: We find that an increase of the attraction strength ...