To convert the given problem description into a symbolic representation and then solve it using Gurobi, we first need to break down the problem into its key components: variables, objective function, and constraints.

### Symbolic Representation:

Let's denote:
- `x0` as the number of intrusion analysts,
- `x1` as the number of automatic alerts.

The objective function is to maximize:
\[4(x_0)^2 + 1(x_0)(x_1) + 6(x_1)^2 + 2(x_0) + 7(x_1)\]

Constraints are as follows:
1. Network latency from intrusion analysts and automatic alerts: 
   - Each intrusion analyst causes 9 ms of additional network latency.
   - Each automatic alert creates 14 ms of additional network latency.
   - The total must be no more than 31 milliseconds.
2. Available bandwidth impact:
   - Intrusion analysts take up 12 bits per second each.
   - Automatic alerts cost 6 bps each.
3. Minimum network latency requirement: 
   - \((x_0 \cdot 9)^2 + (x_1 \cdot 14)^2 \geq 14^2\)
4. Minimum bandwidth usage:
   - \(12x_0 + 6x_1 \geq 9\)
5. Constraint on the number of intrusion analysts and automatic alerts: 
   - \(-2x_0 + 10x_1 \geq 0\)
6. Maximum available bandwidth:
   - \((12x_0)^2 + (6x_1)^2 \leq 41^2\) or simply \(12x_0 + 6x_1 \leq 41\), considering the context.
7. Integer constraints:
   - Both `x0` and `x1` must be integers.

### Symbolic Problem Description:

```json
{
  'sym_variables': [('x0', 'intrusion analysts'), ('x1', 'automatic alerts')],
  'objective_function': '4*(x0)**2 + x0*x1 + 6*(x1)**2 + 2*x0 + 7*x1',
  'constraints': [
    '9*x0 + 14*x1 <= 31', 
    '12*x0 + 6*x1 >= 9', 
    '(9*x0)**2 + (14*x1)**2 >= 196', 
    '-2*x0 + 10*x1 >= 0', 
    '(12*x0)**2 + (6*x1)**2 <= 1681', 
    'x0 == int(x0)', 
    'x1 == int(x1)'
  ]
}
```

### Gurobi Code:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="intrusion_analysts")
x1 = m.addVar(vtype=GRB.INTEGER, name="automatic_alerts")

# Objective function: Maximize
m.setObjective(4*x0**2 + x0*x1 + 6*x1**2 + 2*x0 + 7*x1, GRB.MAXIMIZE)

# Constraints
m.addConstr(9*x0 + 14*x1 <= 31, name="max_network_latency")
m.addConstr(12*x0 + 6*x1 >= 9, name="min_bandwidth_usage")
m.addConstr((9*x0)**2 + (14*x1)**2 >= 196, name="min_network_latency_squared")
m.addConstr(-2*x0 + 10*x1 >= 0, name="analysts_vs_alerts")
m.addConstr((12*x0)**2 + (6*x1)**2 <= 1681, name="max_bandwidth_usage_squared")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Intrusion Analysts: {x0.x}")
    print(f"Automatic Alerts: {x1.x}")
else:
    print("No optimal solution found.")
```