To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- $x_1$ as the number of trips taken by the boat.
- $x_2$ as the number of trips taken by the neighbor.

The objective is to maximize the total number of berries transported, which can be represented as $200x_1 + 40x_2$ since each boat trip can carry 200 units of berries and each neighbor trip can carry 40 units.

The constraints are:
1. The cost constraint: $30x_1 + 8x_2 \leq 500$, because the total cost must not exceed $500.
2. The trip constraint: $x_1 \leq x_2$, because the number of boat trips cannot exceed the number of trips taken by the neighbor.
3. Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$, since the number of trips cannot be negative.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of boat trips'), ('x2', 'number of neighbor trips')],
    'objective_function': 'maximize 200*x1 + 40*x2',
    'constraints': ['30*x1 + 8*x2 <= 500', 'x1 <= x2', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="boat_trips")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="neighbor_trips")

# Set the objective function
m.setObjective(200*x1 + 40*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(30*x1 + 8*x2 <= 500, "cost_constraint")
m.addConstr(x1 <= x2, "trip_constraint")
m.addConstr(x1 >= 0, "non_negativity_boat")
m.addConstr(x2 >= 0, "non_negativity_neighbor")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of boat trips: {x1.x}")
    print(f"Number of neighbor trips: {x2.x}")
    print(f"Total berries transported: {200*x1.x + 40*x2.x}")
else:
    print("No optimal solution found")
```