To solve the given optimization problem using Gurobi, we need to translate the natural language description into a mathematical model that can be represented in code. The problem involves maximizing an objective function subject to several constraints, all of which are related to the amount of carbohydrates from different food items.

The objective function is:
\[6 \times (\text{potatoes})^2 + 7 \times (\text{potatoes}) \times (\text{rotisserie chickens}) + 5 \times (\text{cherry pies})^2 + 4 \times (\text{cherry pies}) \times (\text{rotisserie chickens}) + 2 \times (\text{rotisserie chickens})^2 + 6 \times (\text{rotisserie chickens}) \times (\text{cantaloupes}) + 5 \times (\text{cantaloupes})^2 + 1 \times (\text{potatoes})\]

Constraints:
- Each potato contains 13 grams of carbohydrates.
- Each cherry pie contains 10 grams of carbohydrates.
- Each rotisserie chicken contains 11 grams of carbohydrates.
- Each cantaloupe contains 2 grams of carbohydrates.
- The total carbohydrates from potatoes and cantaloupes must not exceed 21 grams.
- The total carbohydrates from potatoes and cherry pies must not exceed 46 grams.
- The total carbohydrates from all items (potatoes, cherry pies, rotisserie chickens, and cantaloupes) must not exceed 61 grams.
- All quantities (potatoes, cherry pies, rotisserie chickens, cantaloupes) must be integers.

Here's how we can translate these requirements into Gurobi code:

```python
from gurobipy import *

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

# Define variables
potatoes = m.addVar(vtype=GRB.INTEGER, name="potatoes")
cherry_pies = m.addVar(vtype=GRB.INTEGER, name="cherry_pies")
rotisserie_chickens = m.addVar(vtype=GRB.INTEGER, name="rotisserie_chickens")
cantaloupes = m.addVar(vtype=GRB.INTEGER, name="cantaloupes")

# Objective function
m.setObjective(6 * potatoes**2 + 7 * potatoes * rotisserie_chickens + 
               5 * cherry_pies**2 + 4 * cherry_pies * rotisserie_chickens + 
               2 * rotisserie_chickens**2 + 6 * rotisserie_chickens * cantaloupes + 
               5 * cantaloupes**2 + potatoes, GRB.MAXIMIZE)

# Constraints
m.addConstr(13*potatoes + 10*cherry_pies + 11*rotisserie_chickens + 2*cantaloupes <= 61, "carb_total")
m.addConstr(13*potatoes + 2*cantaloupes <= 21, "carb_pot_cant")
m.addConstr(13*potatoes + 10*cherry_pies <= 46, "carb_pot_cherry")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Potatoes: {potatoes.x}")
    print(f"Cherry Pies: {cherry_pies.x}")
    print(f"Rotisserie Chickens: {rotisserie_chickens.x}")
    print(f"Cantaloupes: {cantaloupes.x}")
    print(f"Objective Function Value: {m.ObjVal}")
else:
    print("No optimal solution found")
```