In this research work, we study 𝔮-calculus focusing on the development of quantum estimates involving 𝔮-differentials and 𝔮-integrals. By constructing identities based on these quantum tools, we analyze the structure and behavior of convex functions within 𝔮-calculus.We present generalized formulations of various q-inequalities, offering a foundation for further investigation of different types of integral inequalities in the quantum setting.Our approach highlights the utility of convex function properties in 𝔮-analysis and contributes to the advancement of inequality theory in quantum integral.In our research work, based on quantum analog of Hermite-Hadamard inequality, the quantum analog of some trapezoid, midpoint, Bullen and Simpson type inequalities are established. Moreover, by taking the special selection of κ and s and taking limit 𝔮→1– some new results are obtained, and some old results are verified.