To solve the given optimization problem using Gurobi, we need to translate the natural language description into a mathematical formulation and then implement it in Python using the Gurobi library. The objective function to be maximized is:

\[ 2.08 \times (\text{potatoes})^2 + 2.07 \times (\text{apple pies})^2 + 9.38 \times (\text{apple pies}) \times (\text{kale salads}) \]

Subject to the constraints:

1. Calcium from potatoes, apple pies, and kale salads should not exceed 126 milligrams.
2. Apple pies and kale salads together should not contribute more than 50 milligrams of calcium.
3. Potatoes squared and kale salads squared together should not contribute more than 115 milligrams of calcium.
4. The total calcium from all sources should not exceed 115 milligrams.

Given the variables:
- \( x_0 \) represents the quantity of potatoes,
- \( x_1 \) represents the number of apple pies, which must be an integer,
- \( x_2 \) represents the quantity of kale salads,

And given coefficients:
- Potatoes contain 2.54 milligrams of calcium per unit (\( c_{0} = 2.54 \)),
- Apple pies contain 13.7 milligrams of calcium per unit (\( c_{1} = 13.7 \)),
- Kale salads contain 11.67 milligrams of calcium per unit (\( c_{2} = 11.67 \)),

The constraints can be formulated as:
1. \( 2.54x_0 + 13.7x_1 + 11.67x_2 \leq 126 \)
2. \( 13.7x_1 + 11.67x_2 \leq 50 \)
3. \( (2.54x_0)^2 + (11.67x_2)^2 \leq 115 \)
4. \( 2.54x_0 + 13.7x_1 + 11.67x_2 \leq 115 \)

Here's how you can implement this problem in Gurobi:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
potatoes = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="potatoes")
apple_pies = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="apple_pies")
kale_salads = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="kale_salads")

# Define the objective function
m.setObjective(2.08 * potatoes**2 + 2.07 * apple_pies**2 + 9.38 * apple_pies * kale_salads, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2.54*potatoes + 13.7*apple_pies + 11.67*kale_salads <= 126, name="Total_Calcium_Constraint")
m.addConstr(13.7*apple_pies + 11.67*kale_salads <= 50, name="Apple_Pies_and_Kale_Salads_Calcium_Constraint")
m.addConstr((2.54*potatoes)**2 + (11.67*kale_salads)**2 <= 115, name="Potatoes_and_Kale_Salads_Squared_Calcium_Constraint")
m.addConstr(2.54*potatoes + 13.7*apple_pies + 11.67*kale_salads <= 115, name="Total_Calcium_Constraint_2")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Potatoes: {potatoes.x}")
    print(f"Apple Pies: {apple_pies.x}")
    print(f"Kale Salads: {kale_salads.x}")
else:
    print("No optimal solution found")
```