  We consider trapped bosons with contact interactions as well as Coulomb
repulsion or gravitational attraction in one spatial dimension. The exact
ground state energy and wave function are identified in closed form together
with a rich phase diagram, unveiled by Monte Carlo methods, with crossovers
between different regimes. A trapped McGuire quantum soliton describes the
attractive case. Weak repulsion results in an incompressible Laughlin-like
fluid with flat density, well reproduced by a Gross-Pitaevskii equation with
long-range interactions. Higher repulsion induces Friedel oscillation and the
eventual formation of a Wigner crystal.
