We investigate a quantum integrated communication and computation (QICC) scheme for a single-mode bosonic multiple-access channel (MAC) with coherent-state signalling. By exploiting the natural superposition property of the quantum MAC, a common receiver simultaneously performs over-the-air computation (OAC) on the analogue symbols transmitted by one set of devices and decodes multiple-access data from another. The joint design of the transmit power control and the receive coefficient leads to a non-convex optimization problem that maximizes computation accuracy under a prescribed sum-rate communication constraint. To address this challenge, we develop a low-complexity alternating-optimization framework that incorporates: (i) closed-form linear minimum-mean square error updates for the receive coefficient, (ii) monotonicity properties of the quantum sum-rate constraint, and (iii) projected-gradient refinements for the communication powers. The proposed QICC scheme achieves an effective computation-communication trade-off with fast convergence and low computational complexity.