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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _fav(self, T, rho, A):
 r"""Specific Helmholtz energy of humid air and derivatives Parameters T : float Temperature, [K] rho : float Density, [kg/m³] A : float Mass fraction of dry air in humid air, [kg/kg] Returns ------- prop : dict Dictionary with helmholtz energy and derivatives: * fir, [kJ/kg] * fira: :math:`\left.\frac{\partial f_{av}}{\partial A}\right|_{T,\rho}`, [kJ/kg] * firt: :math:`\left.\frac{\partial f_{av}}{\partial T}\right|_{A,\rho}`, [kJ/kgK] * fird: :math:`\left.\frac{\partial f_{av}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²] * firaa: :math:`\left.\frac{\partial^2 f_{av}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg] * firat: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK] * firad: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²] * firtt: :math:`\left.\frac{\partial^2 f_{av}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²] * firdt: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K] * firdd: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³] References IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 6, http://www.iapws.org/relguide/SeaAir.html """

        water = IAPWS95()
        rhov = (1-A)*rho
        fv = water._derivDimensional(rhov, T)

        air = Air()
        rhoa = A*rho
        fa = air._derivDimensional(rhoa, T)

        fmix = self._fmix(T, rho, A)

        prop = {}
        # Eq T11
        prop["fir"] = (1-A)*fv["fir"] + A*fa["fir"] + fmix["fir"]
        # Eq T12
        prop["fira"] = -fv["fir"]-rhov*fv["fird"]+fa["fir"] + \
            rhoa*fa["fird"]+fmix["fira"]
        # Eq T13
        prop["firt"] = (1-A)*fv["firt"]+A*fa["firt"]+fmix["firt"]
        # Eq T14
        prop["fird"] = (1-A)**2*fv["fird"]+A**2*fa["fird"]+fmix["fird"]
        # Eq T15
        prop["firaa"] = rho*(2*fv["fird"]+rhov*fv["firdd"] +
                             2*fa["fird"]+rhoa*fa["firdd"])+fmix["firaa"]
        # Eq T16
        prop["firat"] = -fv["firt"]-rhov*fv["firdt"]+fa["firt"] + \
            rhoa*fa["firdt"]+fmix["firat"]
        # Eq T17
        prop["firad"] = -(1-A)*(2*fv["fird"]+rhov*fv["firdd"]) + \
            A*(2*fa["fird"]+rhoa*fa["firdd"])+fmix["firad"]
        # Eq T18
        prop["firtt"] = (1-A)*fv["firtt"]+A*fa["firtt"]+fmix["firtt"]
        # Eq T19
        prop["firdt"] = (1-A)**2*fv["firdt"]+A**2*fa["firdt"]+fmix["firdt"]
        # Eq T20
        prop["firdd"] = (1-A)**3*fv["firdd"]+A**3*fa["firdd"]+fmix["firdd"]
        return prop