## Step 1: Define the symbolic representation of the variables
The variables are 'protein bars' and 'strawberries', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the objective function
The objective function to maximize is $9x_1^2 + 9x_1x_2$.

## Step 3: Define the symbolic representation of the constraints
The constraints given are:
- $x_1 \geq 0$ and $x_2 \geq 0$ (implicit, as they represent quantities of items)
- The tastiness rating of protein bars is 13: $13 \leq 13$ (always true, not a constraint)
- There are 8 grams of protein in protein bars: $8 \leq 8$ (always true, not a constraint)
- Protein bars each have a umami index of 3: $3 \leq 3$ (always true, not a constraint)
- Strawberries have a tastiness rating of 14 each: $14 \leq 14$ (always true, not a constraint)
- There are 12 grams of protein in strawberries: $12 \leq 12$ (always true, not a constraint)
- Strawberries have a umami index of 5: $5 \leq 5$ (always true, not a constraint)
- The total combined tastiness rating from protein bars squared and strawberries squared should be no less than 24: $13^2x_1^2 + 14^2x_2^2 \geq 24$
- The total combined grams of protein from protein bars squared and strawberries squared has to be 12 at minimum: $8^2x_1^2 + 12^2x_2^2 \geq 12$
- The total combined umami index from protein bars and strawberries should be no less than 32: $3x_1 + 5x_2 \geq 32$
- Seven times the number of protein bars, plus -10 times the number of strawberries has to be at minimum zero: $7x_1 - 10x_2 \geq 0$
- The total combined tastiness rating from protein bars plus strawberries must be 41 or less: $13x_1 + 14x_2 \leq 41$
- The total combined grams of protein from protein bars and strawberries should be 36 or less: $8x_1 + 12x_2 \leq 36$
- The total combined umami index from protein bars squared and strawberries squared should be less than or equal to 40: $3^2x_1^2 + 5^2x_2^2 \leq 40$
- The total combined umami index from protein bars and strawberries has to be 40 at maximum: $3x_1 + 5x_2 \leq 40$
- $x_1$ is an integer.

## 4: Convert the problem into a Gurobi code
We will use Gurobi to solve this optimization problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="protein_bars", vtype=gp.GRB.INTEGER)  # integer number of protein bars
x2 = m.addVar(name="strawberries")  # any number of strawberries

# Define the objective function
m.setObjective(9 * x1**2 + 9 * x1 * x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(13**2 * x1**2 + 14**2 * x2**2 >= 24, name="tastiness_rating")
m.addConstr(8**2 * x1**2 + 12**2 * x2**2 >= 12, name="grams_of_protein")
m.addConstr(3 * x1 + 5 * x2 >= 32, name="umami_index_min")
m.addConstr(7 * x1 - 10 * x2 >= 0, name="protein_bars_vs_strawberries")
m.addConstr(13 * x1 + 14 * x2 <= 41, name="total_tastiness_rating")
m.addConstr(8 * x1 + 12 * x2 <= 36, name="total_grams_of_protein")
m.addConstr(3**2 * x1**2 + 5**2 * x2**2 <= 40, name="total_umami_index_squared")
m.addConstr(3 * x1 + 5 * x2 <= 40, name="total_umami_index")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Protein bars: {x1.varValue}")
    print(f"Strawberries: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic representation of the problem
```json
{
    "sym_variables": [
        ["x1", "protein bars"],
        ["x2", "strawberries"]
    ],
    "objective_function": "9*x1^2 + 9*x1*x2",
    "constraints": [
        "169*x1^2 + 196*x2^2 >= 24",
        "64*x1^2 + 144*x2^2 >= 12",
        "3*x1 + 5*x2 >= 32",
        "7*x1 - 10*x2 >= 0",
        "13*x1 + 14*x2 <= 41",
        "8*x1 + 12*x2 <= 36",
        "9*x1^2 + 25*x2^2 <= 40",
        "3*x1 + 5*x2 <= 40"
    ]
}
```