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

### Symbolic Representation

Let's define:
- $x_1$ as the number of intrusion analysts,
- $x_2$ as the amount of automatic alerts.

The objective function to maximize is: $9.56x_1 + 5.67x_2$

The constraints are:
1. Data accessibility impact from intrusion analysts and automatic alerts should be at least 100: $0.03x_1 + 0.37x_2 \geq 100$
2. Total computational load should be at least 23 TFLOPs: $0.99x_1 + 1.39x_2 \geq 23$
3. Constraint on intrusion analysts and automatic alerts: $-6x_1 + 2x_2 \geq 0$
4. Maximum total data accessibility impact is 187: $0.03x_1 + 0.37x_2 \leq 187$
5. Maximum total computational load is 80 TFLOPs: $0.99x_1 + 1.39x_2 \leq 80$
6. The number of intrusion analysts must be an integer: $x_1 \in \mathbb{Z}$
7. The amount of automatic alerts must be an integer: $x_2 \in \mathbb{Z}$

### JSON Representation
```json
{
  'sym_variables': [('x1', 'intrusion analysts'), ('x2', 'automatic alerts')],
  'objective_function': '9.56*x1 + 5.67*x2',
  'constraints': [
    '0.03*x1 + 0.37*x2 >= 100',
    '0.99*x1 + 1.39*x2 >= 23',
    '-6*x1 + 2*x2 >= 0',
    '0.03*x1 + 0.37*x2 <= 187',
    '0.99*x1 + 1.39*x2 <= 80'
  ]
}
```

### Gurobi Code
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="intrusion_analysts")
x2 = m.addVar(vtype=GRB.INTEGER, name="automatic_alerts")

# Set the objective function
m.setObjective(9.56*x1 + 5.67*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.03*x1 + 0.37*x2 >= 100, "data_accessibility_impact_min")
m.addConstr(0.99*x1 + 1.39*x2 >= 23, "computational_load_min")
m.addConstr(-6*x1 + 2*x2 >= 0, "intrusion_alerts_constraint")
m.addConstr(0.03*x1 + 0.37*x2 <= 187, "data_accessibility_impact_max")
m.addConstr(0.99*x1 + 1.39*x2 <= 80, "computational_load_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Intrusion Analysts: {x1.x}")
    print(f"Automatic Alerts: {x2.x}")
else:
    print("No optimal solution found")
```