## Step 1: Define the symbolic representation of the variables
The variables are ['squash plants', 'boxwoods', 'zucchini vines', 'basil plants'] which can be represented symbolically as ['x0', 'x1', 'x2', 'x3'].

## Step 2: Create a dictionary mapping symbolic variables to natural language objects
The symbolic variables and their corresponding natural language objects are:
- 'x0': 'squash plants'
- 'x1': 'boxwoods'
- 'x2': 'zucchini vines'
- 'x3': 'basil plants'

## 3: Define the objective function in symbolic notation
The objective function to maximize is: $6x_0^2 + 4x_0x_1 + 7x_0x_2 + 7x_0x_3 + 5x_1^2 + 6x_2^2 + 4x_2x_3 + 5x_3^2 + 2x_0 + 9x_1 + 6x_2 + 8x_3$

## 4: List the constraints in symbolic notation
The constraints are:
- $0.7x_0 \leq 39$
- $0.74x_0 \leq 56$
- $0.34x_1 \leq 39$
- $0.76x_1 \leq 56$
- $0.18x_2 \leq 39$
- $0.55x_2 \leq 56$
- $0.46x_3 \leq 39$
- $0.84x_3 \leq 56$
- $0.74x_0 + 0.84x_3 \geq 13$
- $0.55x_2 + 0.84x_3 \geq 5$
- $0.76^2x_1^2 + 0.84^2x_3^2 \geq 11$
- $0.74x_0 + 0.55x_2 \geq 11$
- $0.76x_1 + 0.55x_2 \geq 10$
- $-4x_0^2 + 7x_2^2 \geq 0$
- $0.34x_1 + 0.46x_3 \leq 35$
- $0.7x_0 + 0.18x_2 \leq 18$
- $0.7x_0 + 0.46x_3 \leq 36$
- $0.7^2x_0^2 + 0.34^2x_1^2 \leq 10$
- $0.7x_0 + 0.34x_1 + 0.18x_2 + 0.46x_3 \leq 10$
- $0.76x_1 + 0.55x_2 \leq 36$
- $0.74x_0 + 0.55x_2 \leq 21$
- $0.76x_1 + 0.84x_3 \leq 16$
- $0.74x_0 + 0.76x_1 \leq 24$
- $0.74x_0 + 0.84x_3 \leq 35$
- $0.74x_0 + 0.76x_1 + 0.55x_2 + 0.84x_3 \leq 35$
- $x_0, x_1, x_2, x_3 \geq 0$ and are integers.

## 5: Convert the problem into Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="squash_plants", vtype=gurobi.GRB.INTEGER)
x1 = model.addVar(name="boxwoods", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="zucchini_vines", vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name="basil_plants", vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(6*x0**2 + 4*x0*x1 + 7*x0*x2 + 7*x0*x3 + 5*x1**2 + 6*x2**2 + 4*x2*x3 + 5*x3**2 + 2*x0 + 9*x1 + 6*x2 + 8*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(0.7*x0 <= 39)
model.addConstr(0.74*x0 <= 56)
model.addConstr(0.34*x1 <= 39)
model.addConstr(0.76*x1 <= 56)
model.addConstr(0.18*x2 <= 39)
model.addConstr(0.55*x2 <= 56)
model.addConstr(0.46*x3 <= 39)
model.addConstr(0.84*x3 <= 56)
model.addConstr(0.74*x0 + 0.84*x3 >= 13)
model.addConstr(0.55*x2 + 0.84*x3 >= 5)
model.addConstr(0.76**2*x1**2 + 0.84**2*x3**2 >= 11)
model.addConstr(0.74*x0 + 0.55*x2 >= 11)
model.addConstr(0.76*x1 + 0.55*x2 >= 10)
model.addConstr(-4*x0**2 + 7*x2**2 >= 0)
model.addConstr(0.34*x1 + 0.46*x3 <= 35)
model.addConstr(0.7*x0 + 0.18*x2 <= 18)
model.addConstr(0.7*x0 + 0.46*x3 <= 36)
model.addConstr(0.7**2*x0**2 + 0.34**2*x1**2 <= 10)
model.addConstr(0.7*x0 + 0.34*x1 + 0.18*x2 + 0.46*x3 <= 10)
model.addConstr(0.76*x1 + 0.55*x2 <= 36)
model.addConstr(0.74*x0 + 0.55*x2 <= 21)
model.addConstr(0.76*x1 + 0.84*x3 <= 16)
model.addConstr(0.74*x0 + 0.76*x1 <= 24)
model.addConstr(0.74*x0 + 0.84*x3 <= 35)
model.addConstr(0.74*x0 + 0.76*x1 + 0.55*x2 + 0.84*x3 <= 35)
model.addConstr(x0 >= 0)
model.addConstr(x1 >= 0)
model.addConstr(x2 >= 0)
model.addConstr(x3 >= 0)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```

## Step 6: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'squash plants'),
        ('x1', 'boxwoods'),
        ('x2', 'zucchini vines'),
        ('x3', 'basil plants')
    ],
    'objective_function': '6*x0^2 + 4*x0*x1 + 7*x0*x2 + 7*x0*x3 + 5*x1^2 + 6*x2^2 + 4*x2*x3 + 5*x3^2 + 2*x0 + 9*x1 + 6*x2 + 8*x3',
    'constraints': [
        '0.7*x0 <= 39',
        '0.74*x0 <= 56',
        '0.34*x1 <= 39',
        '0.76*x1 <= 56',
        '0.18*x2 <= 39',
        '0.55*x2 <= 56',
        '0.46*x3 <= 39',
        '0.84*x3 <= 56',
        '0.74*x0 + 0.84*x3 >= 13',
        '0.55*x2 + 0.84*x3 >= 5',
        '0.76^2*x1^2 + 0.84^2*x3^2 >= 11',
        '0.74*x0 + 0.55*x2 >= 11',
        '0.76*x1 + 0.55*x2 >= 10',
        '-4*x0^2 + 7*x2^2 >= 0',
        '0.34*x1 + 0.46*x3 <= 35',
        '0.7*x0 + 0.18*x2 <= 18',
        '0.7*x0 + 0.46*x3 <= 36',
        '0.7^2*x0^2 + 0.34^2*x1^2 <= 10',
        '0.7*x0 + 0.34*x1 + 0.18*x2 + 0.46*x3 <= 10',
        '0.76*x1 + 0.55*x2 <= 36',
        '0.74*x0 + 0.55*x2 <= 21',
        '0.76*x1 + 0.84*x3 <= 16',
        '0.74*x0 + 0.76*x1 <= 24',
        '0.74*x0 + 0.84*x3 <= 35',
        '0.74*x0 + 0.76*x1 + 0.55*x2 + 0.84*x3 <= 35'
    ]
}
```