## Step 1: Define the symbolic representation of the variables
The variables are ['black beans', 'protein bars', 'cantaloupes', 'potatoes', 'chicken thighs'] which can be represented symbolically as ['x1', 'x2', 'x3', 'x4', 'x5'].

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is: $4.02x_1^2 + 1.5x_1x_2 + 2.97x_1x_4 + 9.14x_2^2 + 6.05x_2x_4 + 3.4x_3^2 + 8.07x_3x_5 + 2.66x_4x_5 + 2.08x_5^2 + 8.24x_1 + 7.75x_3 + 7.02x_4$.

## 3: List the constraints in symbolic notation
The constraints are:
1. $22x_1 + 4x_2 + 10x_3 + 9x_4 + 4x_5 \geq 66$
2. $22x_1 + 4x_2 + 10x_3 + 9x_4 + 4x_5 \geq 66$
3. $-9x_1^2 + 6x_5^2 \geq 0$
4. $10x_3 - 9x_5 \geq 0$
5. $7x_1 - 4x_2 \geq 0$
6. $22^2x_1^2 + 4^2x_2^2 \leq 348$
7. $22x_1 + 9x_4 + 4x_5 \leq 459$
8. $22x_1 + 10x_3 + 9x_4 \leq 285$
9. $4x_2 + 10x_3 + 4x_5 \leq 150$
10. $10x_3 + 9x_4 + 4x_5 \leq 265$
11. $22x_1 + 4x_2 + 4x_5 \leq 382$

## 4: Create a dictionary for the symbolic representation
```json
{
    'sym_variables': [
        ('x1', 'black beans'), 
        ('x2', 'protein bars'), 
        ('x3', 'cantaloupes'), 
        ('x4', 'potatoes'), 
        ('x5', 'chicken thighs')
    ], 
    'objective_function': '4.02*x1^2 + 1.5*x1*x2 + 2.97*x1*x4 + 9.14*x2^2 + 6.05*x2*x4 + 3.4*x3^2 + 8.07*x3*x5 + 2.66*x4*x5 + 2.08*x5^2 + 8.24*x1 + 7.75*x3 + 7.02*x4', 
    'constraints': [
        '22*x1 + 4*x2 + 10*x3 + 9*x4 + 4*x5 >= 66', 
        '-9*x1^2 + 6*x5^2 >= 0', 
        '10*x3 - 9*x5 >= 0', 
        '7*x1 - 4*x2 >= 0', 
        '22^2*x1^2 + 4^2*x2^2 <= 348', 
        '22*x1 + 9*x4 + 4*x5 <= 459', 
        '22*x1 + 10*x3 + 9*x4 <= 285', 
        '4*x2 + 10*x3 + 4*x5 <= 150', 
        '10*x3 + 9*x4 + 4*x5 <= 265', 
        '22*x1 + 4*x2 + 4*x5 <= 382'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

# Define the model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="black_beans", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = m.addVar(name="protein_bars", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x3 = m.addVar(name="cantaloupes", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x4 = m.addVar(name="potatoes", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x5 = m.addVar(name="chicken_thighs", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Objective function
m.setObjective(4.02*x1**2 + 1.5*x1*x2 + 2.97*x1*x4 + 9.14*x2**2 + 6.05*x2*x4 + 3.4*x3**2 + 8.07*x3*x5 + 2.66*x4*x5 + 2.08*x5**2 + 8.24*x1 + 7.75*x3 + 7.02*x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(22*x1 + 4*x2 + 10*x3 + 9*x4 + 4*x5 >= 66)
m.addConstr(-9*x1**2 + 6*x5**2 >= 0)
m.addConstr(10*x3 - 9*x5 >= 0)
m.addConstr(7*x1 - 4*x2 >= 0)
m.addConstr(22**2*x1**2 + 4**2*x2**2 <= 348)
m.addConstr(22*x1 + 9*x4 + 4*x5 <= 459)
m.addConstr(22*x1 + 10*x3 + 9*x4 <= 285)
m.addConstr(4*x2 + 10*x3 + 4*x5 <= 150)
m.addConstr(10*x3 + 9*x4 + 4*x5 <= 265)
m.addConstr(22*x1 + 4*x2 + 4*x5 <= 382)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Black beans: ", x1.varValue)
    print("Protein bars: ", x2.varValue)
    print("Cantaloupes: ", x3.varValue)
    print("Potatoes: ", x4.varValue)
    print("Chicken thighs: ", x5.varValue)
else:
    print("The model is infeasible")
```