## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of vitamin B5' and 'milligrams of vitamin B6', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $1.35x_1^2 + 9.21x_1x_2 + 6.81x_2^2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $2x_1 + 8x_2 \geq 34$ (cardiovascular support index minimum)
- $4x_1 + 8x_2 \geq 41$ is incorrect based on the problem statement, it should be $4^2x_1^2 + 8^2x_2^2 \geq 41$ or simply $16x_1^2 + 64x_2^2 \geq 41$ (cognitive performance index minimum)
- $-6x_1^2 + 3x_2^2 \geq 0$ 
- $2^2x_1^2 + 8^2x_2^2 \leq 84$ or $4x_1^2 + 64x_2^2 \leq 84$ (cardiovascular support index maximum)
- $2x_1 + 8x_2 \leq 84$ (cardiovascular support index maximum)
- $4x_1 + 8x_2 \leq 57$ (cognitive performance index maximum)

## 4: Consider the variable restrictions
$x_1$ can be a decimal, and $x_2$ must be a non-fractional (integer) number.

## 5: Symbolic Representation
```json
{
'sym_variables': [('x1', 'milligrams of vitamin B5'), ('x2', 'milligrams of vitamin B6')],
'objective_function': '1.35*x1^2 + 9.21*x1*x2 + 6.81*x2^2',
'constraints': [
    '2*x1 + 8*x2 >= 34',
    '16*x1^2 + 64*x2^2 >= 41',
    '-6*x1^2 + 3*x2^2 >= 0',
    '4*x1^2 + 64*x2^2 <= 84',
    '2*x1 + 8*x2 <= 84',
    '4*x1 + 8*x2 <= 57'
]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")  # milligrams of vitamin B5
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B6

    # Objective function
    model.setObjective(1.35*x1**2 + 9.21*x1*x2 + 6.81*x2**2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x1 + 8*x2 >= 34, name="cardiovascular_support_min")
    model.addConstr(16*x1**2 + 64*x2**2 >= 41, name="cognitive_performance_min")
    model.addConstr(-6*x1**2 + 3*x2**2 >= 0, name="vitamin_interaction")
    model.addConstr(4*x1**2 + 64*x2**2 <= 84, name="cardiovascular_support_max_quad")
    model.addConstr(2*x1 + 8*x2 <= 84, name="cardiovascular_support_max_lin")
    model.addConstr(4*x1 + 8*x2 <= 57, name="cognitive_performance_max")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin B5: {x1.varValue}")
        print(f"Milligrams of vitamin B6: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```