Is there a way to define a template member in a non-template class?

How about (untested):

class Function_A
{
  public:
    template <typename T> void Evaluate(T parameter)
    {
      T value = std::get<Compute<T>>(computers).Function_B(parameter);
      return T(SomeParameter) * value;
    }

  private:
    double SomeParameter;
    std::tuple<Compute<type_1>, Compute<type_2>> computers;
};

Note: std::pair would work exactly the same as std::tuple here, if you fancy the first/second semantics it adds.

Additionally, note that T(SomeParameter) is a C-style cast, which could be problematic if T is not a class type. Consider T{} or static_cast<T>().

One thing you can do is make C static. If you have

template <typename T> void Evaluate(T parameter)
{
  static Compute<T> C; // only do this once per T now
  T value = C.Function_B(parameter);
  return T(SomeParameter)*value;
}

then when you call Evaluate with type_1 you'll have one version of the function that has C<type_1> in it that will only be constructed the first time the function is called and the same thing happens for type_2.