To solve the given optimization problem using Gurobi, we first need to understand and possibly reformulate the problem into a standard form that can be represented in the Gurobi modeling language. The objective function is to maximize \(9.58 \times (\text{hours worked by Ringo})^2 + 1.36 \times (\text{hours worked by Ringo}) \times (\text{hours worked by Laura})\), subject to several constraints involving computer competence ratings and organization scores for both Ringo and Laura.

Given the problem description, let's denote:
- \(x_0\) as the hours worked by Ringo,
- \(x_1\) as the hours worked by Laura.

The objective function is: \(9.58x_0^2 + 1.36x_0x_1\).

Constraints based on the problem description are:
1. Computer competence rating constraint for Ringo: \(2x_0 \leq 60\),
2. Organization score constraint for Ringo: \(6x_0 \leq 151\),
3. Computer competence rating constraint for Laura: \(12x_1 \leq 60\),
4. Organization score constraint for Laura: \(12x_1 \leq 151\),
5. Combined minimum computer competence rating: \(2^2x_0^2 + 12^2x_1^2 \geq 21\),
6. Combined organization score constraint: \(6x_0 + 12x_1 \geq 61\),
7. Linear constraint involving hours worked: \(8x_0 - 4x_1 \geq 0\),
8. Maximum combined computer competence rating from squared terms: \(2^2x_0^2 + 12^2x_1^2 \leq 46\),
9. Maximum combined computer competence rating from linear terms: \(2x_0 + 12x_1 \leq 46\),
10. Maximum combined organization score from squared terms: \(6^2x_0^2 + 12^2x_1^2 \leq 139\),
11. Maximum combined organization score from linear terms: \(6x_0 + 12x_1 \leq 139\),
12. Integer constraint for Ringo's hours: \(x_0\) must be an integer.

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

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Ringo")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")

# Set the objective function
m.setObjective(9.58*x0**2 + 1.36*x0*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x0 <= 60, "Ringo_computer_rating")
m.addConstr(6*x0 <= 151, "Ringo_organization_score")
m.addConstr(12*x1 <= 60, "Laura_computer_rating")
m.addConstr(12*x1 <= 151, "Laura_organization_score")
m.addConstr(4*x0**2 + 144*x1**2 >= 21, "Combined_min_computer_rating")
m.addConstr(6*x0 + 12*x1 >= 61, "Combined_organization_score")
m.addConstr(8*x0 - 4*x1 >= 0, "Hours_worked_constraint")
m.addConstr(4*x0**2 + 144*x1**2 <= 46, "Max_combined_computer_rating_squared")
m.addConstr(2*x0 + 12*x1 <= 46, "Max_combined_computer_rating_linear")
m.addConstr(36*x0**2 + 144*x1**2 <= 139, "Max_combined_organization_score_squared")
m.addConstr(6*x0 + 12*x1 <= 139, "Max_combined_organization_score_linear")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Ringo: {x0.x}")
    print(f"Hours worked by Laura: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```