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We analyze the Berry phase in III-V semiconductor quantum dots (QDs). We show that the Berry phase is highly sensitive to electric fields arising from the interplay between the Rashba and Dresselhaus spin-orbit (SO) couplings. We report that the accumulated Berry phase can be induced from other available quantum states that differ only by one quantum number of the corresponding spin state. The sign change in the g-factor due to the penetration of Bloch wave functions into the barrier materials can be reflected in the Berry phase. We provide characteristics of the Berry phase for three different length scales (spin-orbit length, hybrid orbital length, and orbital radius). We solve the time-dependent Schro-dinger equation by utilizing the Feynman disentangling technique, and we investigate the evolution of spin dynamics during the adiabatic transport of QDs in the two-dimensional plane. Our results can pave the way to building a topological quantum computer in which the Berry phase can be engineered and be manipulated with the application of the spin-orbit couplings through gate-controlled electric fields.