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In this paper, we simulate the electromagnetic behavior of cable-in-conduit conductors (CICCs) and coils using a 3-D integral formulation of magneto-quasistatic Maxwell's equations, where the superconductors are represented by a power-law. The integral equation is numerically formulated using edge-elements and the nonlinear problem is discretized with a quasi-Newton algorithm. The solution of each iteration step is achieved with an iterative GMRES solver, which benefits from an singular value decomposition of the full matrix representing the integral operator. The model is applied to study the electromagnetic behavior of international thermonuclear experimental reactor (ITER) CICC and coils.